010446   Sivakumar M (Mathematics Dep, Thriuvalluvar Univ, Constituent College of Arts and Science, Tittagudi-606 106, Email: sivamaths.vani_r@yahoo.com) : On 4-total product cordiality of some corona graphs. Int J mathl Combinatorics 2016, 3(Sep), 99-106.

Let f be a map from V(G) to {0, 1, ..., k - 1} where - 26 - k is an integer, 2 ≤ k <≤ |V(G)|. For each edge uv, assign the label f(u)f(v) (mod k). f is called a k-total product cordial labeling of G if |ev_f(i) - ev_f(j)| ≤ 1, i, j ∈ {0,1, ... k - 1} where ev_f(x) denotes the total number of vertices and edges labelled with x(x = 0, 1, 2, ..., k - 1). We investigate the 4-Product cordial labeling behaviour of comb, double comb and subdivision of some corona graphs.

2 tables, 6 ref

010445   Sivagnanam C (General Requirements Dep, College of Applied Sciences - sur, Sultanate of Oman, Email: choshi71@gmail.com) : Nonsplit roman domination in graphs. Int J mathl Combinatorics 2016, 4(Dec), 70-8.

A roman dominating function on a graph G is a function f : V(G) → {0, 1, 2} satisfying the condition that every vertex v 6 V(G) for which f(v) = 0, is adjacent to at least one vertex n with f(u) = 2. The weight, of a. roman dominating function f is the value w (f) = Σ_v∈V f(v). The minimum weight of a roman dominating function is called the roman domination number of G and is denoted by γ R(G). A roman dominating function f is called a nonsplit. roman dominating function if the subgraph induced by the set {v.: f(v) = 0} is connected. The minimum weight, of a nonsplit roman dominating function is called the nonsplit roman domination number and is denoted by γ _nsr(G). In this paper, we initiate a study of this parameter.

7 ref

010444   Shashikala P;Rangarajan R (Studies in Mathematics Dep, Mysore Univ, Manasagangotri, Mysuru-570 006) : Tchebychev and Brahmagupta polynomials and golden ratio: two new interconnections. Int J mathl Combinatorics 2016, 3(Sep), 57-67.

The present paper explores interconnections between sequences related to con-vergents of generalized golden ratios and four kinds of Tchebychev polynomials. By defining and adding Brahrnagupta polynomials of third and fourth kind, the paper also interconnects the four kinds of Brahrnagupta, polynomials to the four kinds of Tchebychev Polynomials respectively. In this way, the present paper provides two spectacular views of Tchebychev polynomials of all four kinds through golden ratio and Brahrnagupta polynomials.

12 ref

010443   Shanker G;Baby S A (Centre for Mathematics and Statistics, School of Basic and Applied Statistics, Central Univ of Punjab, Bathinda, Punjab-151 001, Email: gsp.math1978@gmail.com) : On the Riemann and Ricci curvature of finsler spaces with special (α, β)- metric. Int J mathl Combinatorics 2016, 4(Dec), 61-8.

In this paper, we study the curvature properties of the special (α,β)- metric F = α + ∈β + k β²/α (where ∈, k <93> 0 are constants). We find the expressions for Kiemann curvature and of the special (α,β)-metric, when β the 1- form is a killing form of constant length. We give a characterization of the projective flatness for the special (α, β)- metric.

8 ref

010442   Shah M A;Purohit M;Gulzar M H (Mathematics Dep, Vivekananda Global Univ, Jaipur, Email: shahmushtaq81@gmail.com) : Traffic congestion - a challenging problem in the world. Int J mathl Combinatorics 2016, 2(June), 153-60.

The purpose of this paper is to describe the problems which involves in the reduction of traffic congestion. In particular we use graph theoretical approach which is quite appropriate. We use crossing number technique to reduce traffic congestion. The minimum number of crossing points in a complete graph is given by Cr(Kn) ≤ 1/4 [n/2] [n-1/2] [n-2/2] [N-3/2 ] where [ ] represents greatest integer function. And we illustrate the result - 25 - with counter examples.

4 illus, 16 ref

010441   Riyas A;Geetha K (NO, T.K.M. College of Engineering, Kollam-691 005, Email: riyasmaths@gmail.com) : Study on cayley graphs of non Abelian groups. Int J mathl Combinatorics 2016, 4(Dec), 79-87.

All connected Cayley graphs over Abelian groups are Hamiltonian. However, for Cayley graplis over non-Abeliaii groups, Chen and Quimpo prove in [2] that Cayley graphs over Hamiltonian groups (i.e. non- Abelian groups in which every subgroup is normal) are Hamiltonian. In this paper we discuss a few of the ideas which have been developed to establish the existence of Hamiltoman cycles and paths in the vertex induced subgraphs of Cayley graphs over non-Abeliaii groups.

8 illus, 9 ref

010440   Riyas A;Geetha K (Mathematics Dep, T.K.M. College of Engineering, Kollam-691 005, Email: riyasmaths@gmail.com) : Study on Hamiltonian property of Cayley graphs over non-abelian groups. Int J mathl Combinatorics 2016, 3(Sep), 141-3.

The hamiltonian cycles and paths in Cayley graphs naturally arise in computer science in the study of word hyperbolic groups and automatic groups. All Cayley graphs over abelian groups are always hamiltonian. However, for Cayley graphs over non-abelian groups, Chen and Quimpo prove in [1] that Cayley graphs over group of order pq, where p and q primes are Hamiltonian and in [2] that Cayley graphs over hamiltonian groups (i.e., non-abelian groups in which every subgroup is normal) are always hamiltonian. In this paper we investigate the existence of complete hamiltonian cycles and hamiltonian paths in the vertex induced subgraphs of Cayley graphs over non-abelian groups.

6 ref

010439   Reddy P S K (Mathematics Dep, Siddaganga Institute of Technology, B.H. Road, Tunkur-572 103, Email: reddy_math@yahoo.com) : Radial signed graphs. Int J mathl Combinatorics 2016, 4(Dec), 128-34.

In this paper we introduced a new notion radial signed, graph of a signed graph and its properties are obtained. Also, we obtained the structural characterisation of radial signed graphs. Further, we presented some switching equivalent characterizations.

40 ref

010438   Reddy N P;Raju M C;Varma S V K (Mathematics Dep, S.V. Univ, Tirupati, Andhra Pradesh, Email: suijayakumarvarma@yahoo.co.in) : Effect of aligned magnetic field on unsteady flow between a stretching sheet and oscillating porous plate with constant suction. Int Rev pure appl Math 2017, 13(1), 59-71.

The unsteady MHD flow of an incompressible viscous electrically conducting fluid between two horizontal parallel non conducting plates, where the lower one is stretching sheet and the upper one is oscillating porous plate is studied in the presence - 24 - of an aligned magnetic field. Fluid motion is caused by the stretching of the lower sheet and a constant suction is applied at the upper plate which is oscillating in its own plane. The stretching velocity of the sheet is assumed to be a linear function of distance along the channel. The expressions relating to the velocity distribution are obtained and effects of different values of various physical parameters are calculated numerically and shown graphically.

10 illus, 31 ref

010437   Prasad P M V;Raveendranath P;Prasada Rao D R V (Mathematics Dep, D.K.Govt. Degree College, Nellore) : Effect of thermal diffusion and periodic permeability on MHD convective heat and mass transfer through a porous medium in a vetical channel. Int Rev pure appl Math 2017, 13(1), 51-8.

Authors analyse the mixed convective flow of a viscous incompressible conducting fluid through a porous medium confined in the vertical channel whose walls are maintained at constant temperature and concentration. The dissipative effects are taken in to the energy equation. A uniform magnetic filed of strength H₀ is applied normal to the walls. Also we consider the heat generating source in the energy equation. The momentum, energy and diffusion equations are non dimensionalised to obtain the governing parameters viz, Grashoff number G, Reynolds number R, Darcy Parameter D, Prandtl number P, Heat source Parameter a, Schmidt number Sc, buoyancy ratio N and Eckert number EC. The coupled governing equations have been served using a perturbation technique with EC (<60><60> 1). The velocity, temperature are obtained analytically and the behaviour for different variations in the parameter is discussed computationally. The skin friction and the local rate of heat transfer are calculated numerically for variations in the said parameters.

6 illus, 9 ref

010436   Ponraj R;Narayanan S S (Mathematics Dep, Sri Paramakalyani College, Alwarkurichi-627 412, Email: poonrajmaths@gmail.com) : Radio mean number of certain graphs. Int J mathl Combinatorics 2016, 2(June), 51-64.

A radio mean labeling of a connected graph G is a one to one map f from the vertex set V (G) to the set of natural numbers N such that for each distinct vertices u and v of G, d(u, v) + [f(u)+f(v)/2] ≥ 1 + diarn (G). The radio mean number of f, rmn (f), is the maximum number assigned to any vertex of G. The radio mean number of G, rmn (G) is the minimum value of rmn (f) taken over all radio mean labeling f of G. In this paper we find the radio mean number of Jelly fish, subdivision of jelly fish, book with n pentagonal pages and (K_1,n : m).

7 illlus, 10 ref

010435   Ponraj R;Maria Adaickalam M;Kala R (Mathematics Dep, Sri Paramakalyani College, Alwarkurichi-627 412, Email: ponrajmaths@gmail.com) : k-Difference cordial labeling of graphs. Int J mathl Combinatorics 2016, 2(June), 121-31.

In this paper we introduce new graph labeling called k-difference cordial labeling. Let G be a (p,q) graph and k be an integer, 2 ≤ k ≤ |V(G)|. Let f : V(G) → {1, 2, ..., k} be a map. For each edge uv, assign the label |f(u) - f(v)|. f is called a k-difference cordial labeling - 23 - of G if |v_f(i) - v_f(j)0)| ≤ 1 and e_f(0) - e_f(1)| ≤ 1 where v_f(x) denote the number of vertices labelled with x, e_f(l) and e_f(0) respectively denote the number of edges labelled with 1 and not labelled with 1. A graph with a k-difference cordial labeling is called a k-difference cordial graph. In this paper we investigate k-difference cordial labeling behavior of star, m copies of star and we prove that every graph is a subgraph of a connected k-difference cordial graph. Also we investigate 3-difference cordial labeling behavior of some graphs.

2 illus, 4 tables, 4 ref

010434   Pal B;Dey S;Bhattacharyya A (Mathematics Dep, Institute of Science, Varanasi-221 005) : Spherical chains inside a spherical segment. Int J mathl Combinatorics 2016, 4(Dec), 153-60.

The present paper deals with a. spherical chain whose renters lie on a horizontal piano which can be drawn inside a spherical fragment and we display some geometric properties related to the chain itself. Here, we also grant recursive and non recursive formulas for calculating the coordinates of the centers and the radii of the spheres.

5 illus, 2 ref

010433   Om Prakash;Gandhi G P (Mathematics Dep, Guru Nanak Dev Univ, Amritsar-143 005, Email: omprakash777@yahoo.co.in) : New measures of information based upon measures of central tendency and dispersion. Int Rev pure appl Math 2017, 13(1), 23-34.

In this paper, we have developed some probabilistic measures of information based upon measures of central tendency, namely, arithmetic mean, geometric mean and harmonic mean. We have also extended this theory for the development of measures of information involving measures of central tendency, dispersion and other means like power mean, exponential mean and quadratic mean etc.

4 illus, 1 table, 15 ref

010432   Nellai Murugan A;Iyadurai Selvaraj P (Mathematics Dep, V.O. Chidambaram College, Tamil Nadu, Email: anellai.vocc@gmail.com) : Cycle and armed cap cordial graphs. Int J mathl Combinatorics 2016, 2(June), 144-52.

Let G = (V,E) be a graph with p vertices and q edges. A Cap (∧) cordial labeling of a Graph G with vertex set V is a bijection from V to 0,1 such that if each edge uv is assigned the label [f (uv) = {1, if f(u)=f(v)=l, or 0, otherwise] with the condition that the number of vertices labeled with 0 and the number of vertices labeled with 1 differ by at most 1 and the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. Otherwise, it is called a Smarandache A cordial labeling of G. A graph that admits a A cordial labeling is called a ∧ cordial graph (CCG). In this paper, we proved that cycle C_n (n is even), bistar B_m,n, P_m ∙ P_n and Helm are A cordial graphs.

10 illus, 7 ref

010431   Narayanan S R;Murugesan S (Mathematics Dep, Karpaga Vinayaga College of Engineering and Technology, Chennai, Tamil Nadu, Email: ravimathsdept@gmail.com) : 2-Pseudo neighbourly irregular intuitionistic fuzzy graphs. Int J mathl Combinatorics 2016, 4(Dec), 8-20.

In this paper. 2-pseudo neighbourly - 22 - irregular intuitionistic fuzzy graph, 2-pseudo neighbourly totally irregular intuitionistic fuzzy graph are introduced and compared through various examples. A necessary and sufficient condition under which they are equivalent is provided. 2- pseudo neighbourly irregularity on some intuitionistic fuzzy graphs whose underlying crisp graphs are a cycle C_n, a Bi-star graph B_n,m, Sub(B_n,m), and a path P_n, are studied.

2 illus, 16 ref

010430   Narayana N S (N.E.S. Ratnam College of Arts, Science and Commerce, Bhandup, Mumbai-400 078, Email: narayana_nithya@yahoo.com) : Tutte polynomial of generalized flower graphs. Int J mathl Combinatorics 2016, 2(June), 29-42.

The book graph denoted by B_{n,2 is the Cartesian Product Sn+1 x P2} where 5_n+1 is a star graph with n vertices of degree 1 and one vertex of degree n and P₂ is the path graph of 2 vertices. Let X_n,p denote the generalized form of Book graph where a family of p cycles which are n in number, is merged at a common edge. The generalized flower graph is obtained by merging t copies of X_n,p with a base cycle C_t of length t at the common edges. The resultant structure looks like flower with petals. In this paper we discuss some properties satisfied by Tutte polynomial of this special graph and the related graphs.

5 illus, 8 ref

010429   Nagesh H M;Chandrasekhar R;Mahesh Kumar M C (NO, PES Institute of Technology (Bangalore South Campus), Bangalore-560 100, Email: nageshhm@pes.edu.dr) : Directed pathos block line cut-vertex digraph of an arborescence. Int J mathl Combinatorics 2016, 4(Dec), 144-52.

For an arborescence T, a directed pathos block line cut-vertex digraph Q = DPBL_c(T) has vertex set, V(Q) = A(T) U C(T) U B(T) U P(T), where C(T) is the cut-vertex set, D(T) is the block set, and P(T) is a directed pathos set of T. The arc set A(Q) consists of the following arcs: ab such that a, ft ∈ A(T) and the head of a coincides with the tail of 6: Cd such that C ∈ C(T) and d ∈, 4(T) and the tail of d is C: dC such that, G' ∈ C'(T) and d ∈ A(T) and the head of d is C; Be such that B 6 B(T) and c ∈ A1(T) and the arc c lies on the block B; Pa such that a ∈ A(T) and P ∈ P(T) and the arc a lies on the directed path P; P_iP_j such that P_i,P_j ∈ P(T) and it is possible to reach the head of P_j from the tail of P; through a common vertex, but it, is possible to reach the head of P, from the tail of P_j. The problem of reconstructing an arborescence from its DPBL_c(T) is discussed. We present the characterization of digraphs whose DPRL_c(T) are planar and outer planar. In addition, a. necessary and sufficient, condition for DPBL_c(T) to have crossing number one is presented. Further we show that for any arborescence T, DPDL_c(T) never be maximal outer planar and minimally nonouterplanar.

8 ref

010428   Mirajkar K G;Priyanka Y B (Mathematics Dep, Karnatak Arts College, Dharwad-580 001) : Traversability and covering invariants of Toiken graphs. Int J mathl Combinatorics 2016, 2(June), 132-8.

Let F_k(G),k ≥ 1, G be the token graph of a connected graph G. In this paper, we investigate the Eulerian and Hamiltoniau property of token graphs and obtain the covering invariants for complete graph of token graph.

10 ref

010427   Mathew Varkey T K;Sunoj B S (Mathematics Dep, T.K.M. College of Engineering, Kollam-5, Email: mathewvarkeytk@gmail.com) : Some new families of odd graceful graphs. Int J mathl Combinatorics 2016, 3(Sep), 158-61.

A labeling or numbering of a graph G is an assignment f of labels to the vertices of G that induces for each edge uv a labeling depending on the vertex labels f(u) and f(v). In this paper we study some new families of odd graceful graphs.

4 illus, 3 ref

010426   Mathew Varkey T K;Rajesh Kumar T J (Mathematics Dep, T.K.M College of Engineering, Kollam, Kerala) : Note on neighborohood prime labeling. Int J mathl Combinatorics 2016, 4(Dec), 161-7.

A labeling or numbering of a graph G is an assignment of labels to the vertices of G that inducts for each edge uv a labeling depending on the vertex labels f(u) and f(v). In this paper, we investigate neighborhood prime labeling of graph obtained by identifying any two vertices of path P_n. We also discuss neighborhood prime labeling in some graph operations on the cycle C_n.

10 ref

010425   Mak M;Altnbas H (Mathematics Dep, Ahi Evran Univ, The Faculty of Arts and Sciences, Kirsehir, Turkey) : Spacelike smarandache curves of timelike curyes in anti de sitter 3-space. Int J mathl Combinatorics 2016, 3(Sep), 1-16.

In this paper, we investigate special spacelike Smarandache curves of timelike curves according to Sabban frame in Anti de Sitter 3-Space. Moreover, we give the relationship between the base curve and its Smarandache curve associated with theirs Sabban Frames. However, we obtain some geometric results with respect to special cases of the base curve. Finally, we give some examples of such curves and draw theirs images under stereographic projections from Anti de Sitter 3-space to Minkowski 3-space.

1 illsu, 12 ref

010424   Maheswari N R S (Mathematics Dep, G. Venkataswany Naidu College, Kovilpatti-628 502, Email: nrsmaths@yahoo.com ) : On m-neighbourle irregular instuitionistic fuzzy graphs. Int J mathl Combinatorics 2016, 3(Sep), 107-14.

In this paper, m-neighbourly irregular intuitionistic fuzzy graphs and m-neighbourly totally irregular intuitionistic fuzzy graphs are defined. Relation between rn-neighbourly irregular intuitionistic fuzzy graph and m-neighbourly totally irregular intuitionistic fuzzy graph are discussed. An m-neighbourly irregularity on intuitiouistic fuzzy graphs whose underlying crisp graphs are cycle C_n, a path P_n are studied.

3 illus, 20 ref

010423   Lv X;Yan Z;Wei E (Mathematics Dep, Renmin Univ of China, Beijing 100872, P.R. China, Email: werling@ruc.edu.cn) : Merrifield-Simmons indices of triangle-trees with k pendant-triangles. Int J mathl Combinatorics 2016, 2(June), 92-100.

Triangle-trees are a kind of graphs derived from Koch networks. The Merrifield-Simmons index of a graph is the total number of the independent sets of the graph. We prove that P^Δ_k,n-k is the triangle-tree with maximal Merrifield-Sirnmons index among all the triangle-trees with n triangles and k pendant triangles.

5 illus, 13 ref

010422   Lourdusamy A;Mathivanan T (Mathematics Dep, St. Xavier's College (Autonomous), Palayankottai-627 002, Email: lourdusamy15@gmail.com) : The pebbling number of Jahangir graph J_2,m. Int J mathl Combinatorics 2016, 3(Sep), 86-98.

The t-pebbling number. f_t(G), of a connected graph G, is the smallest positive integer such that from every placement of f_t(G) pebbles, t pebbles can be moved to any specified target vertex by a sequence of pebbling moves, each move taking two pebbles off a vertex and placing one on an adjacent vertex. When t = 1. we call it as the pebbling number of G, and we denote it by f(G). In this paper, we are going to give an alternate proof for the pebbling number of the graph J_2,m (m ≥ 3).

13 ref

010421   Linfan M A O (NO, Chinese Academy of Mathematics and System Science, Beijing 100190, P.R. China) : Labeled graph-a mathematical element. Int J mathl Combinatorics 2016, 3(Sep), 27-56.

The universality of contradiction and connection of things in nature implies that a thing is nothing else but a labeled topological graph G^{L with a labeling map L : V(G) U E(G) -L in space, which concludes also that labeled graph should be an element for understanding things in the world. This fact proposes 2 directions on labeled graphs: (1) verify a graph family & whether or not they can be labeled by a labeling L constraint on special conditions, and (2) establish mathematical systems such as those of groups, rings, linear spaces or Banach spaces over graph G, i.e., view labeled graphs GL as elements of that system. However, all results on labeled graphs are nearly concentrated on the first in past decades, which is in fact searching structure G of the labeling set L. The main purpose of this survey is to show the role of labeled graphs in extending mathematical systems over graphs G, particularly graphical tensors and G(bar) flows with conservation laws and applications to physics and other sciences such as those of labeled graphs with sets or Euclidean spaces R" labeling, labeled graph solutions of non-solvable systems of differential equations with global stability and extended Banach or Hilbert G-flow spaces. All of these makes it clear that holding on the reality of things by classical mathematics is partial or local, only on the coherent behaviors of things for itself homogenous without contradictions, but the mathematics over graphs G is applicable for contradictory systems over G because contradiction is universal in the nature, which can turn a contradictory system to a compatible one, i.e.. mathematical combinatorics.}

22 illus, 32 ref

010420   Li Y (Mathematics Dep, Huizhou Univ, Huizhou 516007, P.R. China, Email: liya820615@126.com) : Grobner-Shirshov bases theory for the right idelas of left-commutative algebras. Int J mathl Combinatorics 2016, 4(Dec), 53-60.

In this paper, we establish a Composition-Diamond lemma for the right ideals of free left-cornrnutative algebras. As an application, we prove that the membership problems for the right ideals of free left-commutative algebras are decidable.

35 ref

010419   Kanna M R R;Pradeep Kumar R;Jamil M K; Farahani M R (Mathematics Dep, Maharani's Science College for Women, Mysore, Karnataka, Email: mrfarahani88@gmail.com) : Eccentricity atom-bond connectivity index of polycyclic armoatic hydrocarbon PAH_k. Int J pharm Sci Res 2017, 8(1), 201-6.

Let G=(V,E) be molecular graph with vertex set V (G) and edge set E(G) in which the set of vertices and the set of edges of the graph correspond to the atoms of the molecule and chemical bonds, respectively. We denote d(u,v) the distance between u and v i.e the length of the shortest path connecting u and v. The eccentricity of a vertex in V(G) is defined to be ε(v) = {max d(u,v); u ∈ V(G)}. Recently, we proposed the fifth atom-bond connectivity index of a simple connected graph G as ABC₅(G). In - 19 - this paper, we present more study of the fifth atom-bond connectivity index and compute this new index of polycyclic aromatic hydrocarbons.

58 ref

010418   Kaliraj K;Sivakami R;Vernold Vivin J (NO, Ramanujan Institute for Advanced Study in Mathematics, Madras Univ, Chepauk, Chennai-600 005) : Star edge coloring of corona product of path with some graphs. Int J mathl Combinatorics 2016, 3(Sep), 115-22.

A star edge coloring of a graph G is a proper edge coloring of G, such that any path of length 4 in G is not bicolored, denoted by X'_st (G), is the smallest integer k for which G admits a star edge coloring with k colors. In this paper, we obtain the star edge chromatic number of P_m o P_n, P_m o S_n, P_m o K_1,n,n and P_m o K_m,n.

10 ref

010417   John T L;Mathew Varkey T K (Mathematics Dep, T.K.M. College of Engineering, Kollam-691 005, Email: teenavinu@gmail.com) : Different labelings on parallel transformations of a class of trees. Int J mathl Combinatorics 2016, 2(June), 139.

A graph G = (V, E) with p vertices and q edges is said to be a mean graph if there exists an injective function f : V → {0, 1, ..., q} that induces an edge labeling f* : E → (1, 2, ..., q} defined by f*(uv) = f(u) + f(v)/2 if f(u) + f(v) is even, or = [f(u) + f(v) + 1]/2 if f(u) + f(v) is odd, for every edge uv; of G. Further f is called a super-mean labeling if f(V(G)) ∪ {f*(e) : e ∈ E(G)} = {1, 2, ..., p + q}. If the vertex labels are all even numbers in {2, 4, ..., 2q} so that f*(e) = [f(u)+f(v)]/2 than f is an even mean labeling of G and if the vertex labels are in {1, 3, ..., 2q - 1} so that f*(e) - [f(u)+f(v)+1]/2 then G is an odd-mean graph. In this paper, we investigate a typical class of trees based on this definition.

2 illus, 5 ref

010416   Farahani M R;Pradeep Kumar R;Kanna M R R (Applied Mathematics Dep, Iran Univ of Science and Technology (IUST) Narmak, Tehran, 16844, Iran, Email: mr_farhani@mathdep.iust.ac.ir) : First and second zagreb indices and polynomials of v-phenylenic nanotubes and nanotori. Int J pharm Sci Res 2017, 8(1), 330-3.

Let G be a simple molecular graph with vertex and edge sets V(G) and E(G), respectively. In 1972, Gutman and Trinajstic introduced the First and Second Zagreb topological indices of molecular graphs. These topological indices are useful in the study of anti-inflammatory activities of certain chemical instances, and in elsewhere. In this present study, compute the First Zagreb index and Second Zagreb index and the First Zagreb polynomial and the Second Zagreb polynomial of V-Phenylenic Nanotubes and Nanotori.

44 ref

010415   Ergun E;Galiskan M (Ondokuz Mayis Univ, Carsamba Chamber of Commerce Vocational School, Samsun, Turkey, Email: eergun@omu.edu.tr) : Ruled surface pair generated by darboux vectors of a curve and its natural lift in R<. Int J mathl Combinatorics 2016, 2(June), 16-28.

In this study, firstly, the darboux vector W of the natural lift α of a curve a are calculated in terms of those of a in R³₁. Secondly, we obtained striction lines and distribution parameters of ruled surface pair generated by by Darboux vectors of the curve α and its natural lift α. Finally, for a and αthose notions are compared with each other.

3 illus, 18 ref

010414   El-Deen M R Z (Mathematics Dep, Faculty of Science, Suez Univ, Suez, Egypt, Email: mohamed.zeeneldeen@Suezuniv.edu.eg ) : Folding of Cayley graphs. Int J mathl Combinatorics 2016, 2(June), 83-91.

The aim of this paper is to discuss the folding of Cayley graphs of finite group. We prove that, for any finite group G, |G| = n and H is a subgroup of G. Then Cayley graph F = Cay(G, S) of G with respect to S = H{1_G} can be folded into a complete graph K_r where r = |H|. Hence every Cayley graph Γ = Cay(G, S) of valency n-1 can not be folded. Also every Cayley graph Γ = Cay((G, S) of valency one can be folded and Γ = Cay(G, S), where S is generating set, every elements in it is self inverse and |S| = 1/2|G|, can be folded to an edge. Theorems governing these types of foldings are achieved.

5 illus, 9 ref

010413   Dutta T;Bhattacharyya A;Debnath S (Mathematics Dep, Jadavpur Univ, Kolkata-700 032) : Conformal ricci soliton in almost C(λ) manifold. Int J mathl Combinatorics 2016, 3(Sep), 17-26.

In this paper we have studied conformal curvature tensor, Ricci curvature tensor, projective curvature tensor in almost C(λ) manifold admitting conformal Ricci soliton. We have studied conformally semi symmetric almost C(λ) manifold admitting conformal Ricci soliton. We have found that a Ricci conharmonically symmetric almost C(λ) manifold admitting conformal Ricci soliton is Einstein manifold. Similarly we have proved that a conformally symmetric almost C(λ) manifold M with respect to projective curvature tensor admitting conformal Ricci soliton is η-Einstein manifold. We have studied Ricci protectively symmetric almost C(λ) manifold also.

11 ref

010412   Dubey S N (Engineering Mathematics Dep, Gyan Ganga Institute of Technology & Sciences, Jabalpur) : Approximation by Fejer operator. Int Rev pure appl Math 2017, 13(1), 15-18.

The present paper embodies the notion of the approximation of a 2π-periodic continuous function satisfying a Lipschitz condition of order a with constant M, i.e. Lip_M α for 0 <60> α <60> 1 by Fejer operator. As a matter of course, our result may be deemed to be a quantitative version of Fejer's Theorem. Constants of approximation have inter alia been taken into notice quite meticulously.

8 ref

010411   Dubey S N (Engineering Mathematics Dep, Gyan Ganga Institute of Technology & Sciences, Jabalpur) : Modulus of continuity & approximation. Int Rev pure appl Math 2017, 13(1), 11-14.

The present paper altogether concentrates upon the study of the quantitative version of convergence of the partial sums S_n(f, x) of the Fourier series to f(x). In point of fact, we have essentially determined the rate at which S_n(f, x) converge to f(x) in terms of modulus of continuity.

7 ref

010410   Deshmukh U;Shaikh V Y (Mathematics Dep, Mithibai College, Vile Parle, Email: ujwala.deshmukh@rediffmail.com) : Mean cordial labelling some star-related graphs. Int J mathl Combinatorics 2016, 3(Sep), 146-57.

Let f be a map from V(G) to {0, 1, 2}. For each edge uv assign the label f*(uv) = [{f(u)+ f(v)}/2}]. f is called as a mean cordial labelling if |v_f(i)- v_f(j)| ≤ 1 and |e*_f(i) - e*_f(j)| ≤ 1, i, j ∈ {0, 1,2}, where v_f(x) and e*_f(x) denote the number of vertices and edges respectively labelled with x (x = 0, 1, 2). A graph with mean cordial labelling is called mean cordial. In this paper we prove the graph <193>K_1,n : 2<209> and path union of n copies of star K_1,m are mean cordial graphs.

6 illus, 5 ref

010409   Dertli A;Cengellenmis Y;Eren S (Mathematics Dep, Faculty of Arts and Sciences, Ondokuz Mayis Univ, Samsun, Turkey) : On linear codes over a non-chain ring. Int J mathl Combinatorics 2016, 2(June), 101-8.

In this paper, we study skew cyclic and quasi cyclic codes over the ring S = F₂ + uF₂ + vF₂ where u² = u, v² = v, uv = vu = 0. We investigate the structural properties of them. Using a Gray map on S we obtain the Mac Williams identities for codes over S. The relationships between Symmetrized. Lee and Hamming weight enumerator are determined.

15 ref

010408   Chen Y;Tian J (Mathematics Dep, Huizhou Univ, Huizhou, Guangdong, 516007, China, Email: yizhichen1980@126.com) : On linear operators preserving othogonality of matrices over fuzzy semirings. Int J mathl Combinatorics 2016, 4(Dec), 88-96.

In thin paper, we investigate the linear operators preserving orthogonality of matrices over fuzzy semirings. We firstly characterize invertible linear operators preserving orthogonality of fuzzy matrices. And then, based on the obtained results, we study the invert ible linear operators preserving orthogonality of matrices over the direct, product of fuzzy semirings, and give some complete characterizations.

21 ref

010407   Chandran S V U;Jaya Parthasarathy G G J (Mathematics Dep, Mahatma Gandhi College, Kesavadasapuram, Pattom P.O., Thiruvanathapuram-695 004, Email: svuc.math@gmail.com) : Geodesic irredundant sets in graphs. Int J mathl Combinatorics 2016, 4(Dec), 135-43.

For two vertices u and v of a connected graph (7, the set I[u, v] consists of all those vertices lying on u - v geodesies in G. Given a set S of vertices of G. the union of all sets I[u, v] for u.v ∈ S is denoted by I[S]. A convex set S satisfies 1[S] = S. The convex hull [S] of S is the smallest convex set containing S. The hull number h(G) is the minimum cardinality among the subsets S of V with [S] = V. In this paper, we introduce and study the geodesic irredundarit number of a graph. A set S of vertices of G is a geodesic irredundant set if u ∉: I[S - {u}} for all u ∈ S and the maximum cardinality of a geodesic irredudant set is its irreduridant number gir (G) of G. We determine the irredundaut number of certain standard classes of graphs. Certain genera.] properties of these concepts are studied. We characterize the classes of graphs of order - 16 - n for which gir(G) = 2 or gir(G} = n or gir(G) = n - 1, respectvely. We prove that for any integers a and b with 2 ≤ α ≤ b, there exists a connected graph G such that h(y) = a and gir (G) = b. A graph H is called a maximum irredundant subgraph if there exists a graph G containing H as induced subgraph such that V(H) is a maximum irredundant set in G. We characterize the class of maximum irredundant subgraphs.

3 illus, 8 ref

010406   Baskar Babujee J;Joshi A (Mathematics Dep, Anna Univ Chennai, Chennai, Email: baskarjee@yahoo.com) : Wiener polynomial for tensor product of graphs. Int Rev pure appl Math 2017, 13(1), 35-42.

Wiener Index is a graph invariant introduced originally for molecular graphs of alkanes. All structural formulas of chemical compounds are molecular graphs where vertices represent the set of atoms and edges represent chemical bonds. The construction and investigation of topological indices that could be used to describe molecular structures is one of the important directions of mathematical chemistry. The Wiener Index W(G) of a graph G is defined as the half of the minimum distances between every pair of vertices of G. As such there is no exact formula to determine the value of W(G) though there are some for particular classes of graphs. In this paper we determine Wiener index and polynomial for some Tensor product graphs.

4 illus, 4 ref

010405   Basavanagoud B;Kulli V R;Teli V V (Mathematics Dep, Karnatak Univ, Dharwad-580 003, Email: b.basavanagoud@gmail.com) : Entire equitable dominating graph. Int J mathl Combinatorics 2016, 2(June), 43-50.

The entire equitable dominating graph EE_qD(G) of a graph G with vertex set V U S, where S is the collection of all minimal equitable dominating sets of G and two vertices u, v ∈ V U S are adjacent if w, v are not disjoint minimal equitable dominating sets in S or u, v ∈ D, where D is the minimal equitable dominating set in S or u ∈ V and v is a minimal equitable dominating set in 5 containing u. In this paper, we initiate a study of this new graph valued function and also established necessary and sufficient conditions for EE_qD(G) to be connected and complete. Other properties of EE_qD(G) are also obtained.

1 illus, 13 ref

010404   Azari M (Mathematics Dep, Kazerun Branch, Islamic Azad Univ, P.O. Box: 73135-168, Kazerun, Iran) : Some results on vertex version and edge versions of modified Schultz index. Int J mathl Combinatorics 2016, 2(June), 65-82.

Let G₁ and G₂ be two simple connected graphs with disjoint vertex sets V(G₁) and V(G₂), respectively. For given vertices α₁ ∈ V(G₁) and α₂2 ∈ V(G₂), a splice of G₁ and G₂ by vertices α₁ and α₂ is defined by identifying the vertices 01 and α₂ in the union of G₁ and G₂ and a link of G₁ and G₂ by vertices α₁ and α₂ is obtained by joining α₁ and α₂ by an edge in the union of these graphs. The modified Schultz index of a simple - 15 - connected graph G is defined as the sum of the terms d(u|G)d(v|G)d(u,v|G) over all unordered pairs {u, v} of vertices in G, where d(u|G) and d(u, v|G) denote the degree of the vertex u of G and the distance between the vertices u and v of G, respectively. In this paper, explicit formulas for computing the vertex and edge-modified Schultz indices of splice and link of graphs are presented.

20 ref

010403   Ayyappan G;Velmurugan S (Mathematics Dep, Pondicherry Engineering College, Puducherry-605 014) : Nonpreemptive priority multiserver queueing system with accessible and non-accessible bulk service and heterogeneous arrivals. Int Rev pure appl Math 2017, 13(1), 73-84.

In this paper a multiserver non-preemptive priority queueing system consisting of two types of customer units with Poisson arrival and exponential service time distribution is analysed. The lower priority units are served by a bulk service rule. This rule admits each batch served to have not less than 'a' and not more than 'b' customers such that the arriving customers can enter service station without affecting the service time if the size of the batch being served is less than 'd' (a ≤d≤b). The higher priority units have non-preemptive priority over lower priority units. The higher priority units are served singly. The steady state probability vectors of the number of customers in the queue are obtained using the modified matrix geometric method. The stability condition and mean queue length of customers are obtained. Numerical results are also presented.

7 ref

010402   Anitha R;Sangavai K (Mathematics and Computer Applications Dep, PSG College of Technology, Coimbatore, Tamil Nadu, Email: anitha_nadarajan@mail.psgtech.ac.in) : Quick survey on the solutions of degree constrained minimum spaning tree problem. Int Rev pure appl Math 2017, 13(1), 19-22.

A spanning tree of a graph such that each node in the tree has degree at most d is called a degree constrained spanning tree. The problem of finding the degree constrained spanning tree of minimum cost in an edge weighted graph is NP-complete for every d, in the range [2, n - 2], where n denotes the number of nodes. In this paper we give a brief summary on the solutions of this problem. This will serve as a complete reference for the people who are interested in doing research in this area.

9 ref

010401   Altintas I;Taskopru K (Faculty of Arts and Sciences, Mathematics Dep, Sakarya Univ, Sakarya, 54187, Turkey, Email: ialtiutas@sakarya.edu.tr) : Generalization of the alexander polynomial. Int J mathl Combinatorics 2016, 4(Dec), 21-8.

In this paper, we present a generalization of two variables of the - 14 - Alexander polynomial for a given oriented knot diagram. We define the Alexander polynomial of two variables by an easy method which will be achieved as a result of the interpretation of the crossing point as a particle with input-output spins in the mathematical physics. The classical Alexander polynomial is the case of one of the variables to be equal to 1 in the Alexander polynomial of two variables.

6 illus, 16 ref

010400   Alilo A;Amjadi J;Vaez Moosavi N;Mohammadikhah S (Mathematics Azarbaijan Dep, Shahid Madani Univ Tabriz, IR, Iran) : Projective dimension and Betti number of some graphs. Int J mathl Combinatorics 2016, 4(Dec), 109-17.

Let G be a graph. Then (G); denotes a graph sucli that to every vertex addes i pendant edges. In this paper, we study the projective dimension and Betti number of some graph such as (S_a')_i, (K_m,_n), ....

2 illus, 12 ref

010399   Adiga C;Rakshith B R;Sumithra;Anitha N (Studies in Mathematics Dep, Mysore Univ, Manasagangorhti, Mysuru-570 006, Email: c.ndiga@hotmail.com) : On wiener and weighted wiener indiced of neighborohood corona of two graphs. Int J mathl Combinatorics 2016, 4(Dec), 97-108.

In this paper, we compute the Wiener index, degree distance index and Gutman index of neighborhood corona, of two graphs.

1 illus, 19 ref

009423   Widodo B;Imron C;Asiyah N;Siswono G O; Rahayuningsih T;Purbandini (Mathematics Dep, Faculty of Mathematics and Natural Science, Institut Teknologi Sepuluh, Surabaya, Indonesia) : Viscoelastic fluid flow pass a porous circular cylinder when the magnetic field included. Far East J mathl Sci 2016, 99(2), 173-86.

This paper is concerned with the boundary layer flow of steady incompressible and viscoelastic fluid (MHD) passing over horizontal porous circular cylinder. The effect of magnetic field that acts on the fluid is applied and the fluid is assumed to be flowing in a porous medium. Governing equations are built from the physical phenomena, i.e., from the continuity equation, the momentum equation and the energy equation. These dimensional governing equations are further reduced by using boundary layer theory and they are converted into non-dirnensional form by substituting non-dimensional variables. Further, these non-dimensional equations are transformed into similar equations and then are solved numerically by using finite difference method. Computational results for the flow quantities are presented graphically. We obtain that the temperature profiles increase when both of mixed convection and magnetic parameters increase. The velocity profiles increase when both of mixed convection and magnetic parameters increase.

5 illus, 22 ref

009422   Udayabaskaran S;Karthikeyan T;Krishnan A E (Mathematics Dep, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Techno, Avadi, Chennai-600 062, Email: udayabaskaran.s@gmail.com) : Spatio-temporal dynamics of a cylindrical neuron subject to a stochastic noise. Far East J mathl Sci 2016, 99(2), 187-204.

A cylindrical model of a neuron is considered to study the dynamics of the depolarization subject to random current injection controlled by a random medium. The random current injection is assumed to be a piecewise white-noise process controlled by a two-state Markov process. For the case of sealed end boundary conditions and for an initial resting state, expressions in the form of infinite series few the expectation, variance, spatial and temporal covariances of the depolarization are obtained.

4 illus, 2 tables, 16 ref