Bulletin of the International Mathematical Virtual Institute

413-421

Authors: Duško Jojić

We use a concrete shelling order of chessboard complexes
n;m for m > 2n

213-219

Authors: K. Pattabiraman

In this paper, we compute the formulae for the third Zagreb indices and its coindices for two classes of graphs such as edge corona product graph, double graph and kth iterated double graph.

233-243

Authors: Guantie Deng, Huaping Huang, Marija Cvetkovic, Stojan Radenovic

The purpose of this article is to introduce the notion of cone valued measure of noncompactness. Our theoretical approach generalizes recent results for cone measure of noncompactness. For the proofs of our results we use the famous Schauder-Tichonov Theorem as well as Robert Cauty theorem in the new framework.

259-270

Authors: Berhanu Assaye Alaba and Yohannes Gedamu Wondifraw

In this paper we introduce the concept of ideals, filters and congruences in a GADFL and we give an equivalent condition for a GADFL to become an ADFL interms of ideals, lters and congruence relations. We also characterize Subdirectly Irreducible GADFLs.

279-285

Authors: Mujeeb Ur Rahman and Mohammad Sarwar

In this paper, we introduce contractive conditions of integral type in the setting of dislocated quasi b-metric spaces. Using contractive conditions of integral type, we have presented a fixed point theorem in the framework of dislocated quasi b-metric spaces. Our established result generalize and extend various fixed point theorems of the literature in the context of dislocated quasi b-metric spaces. An example is given in the support of our main results.

301-314

Authors: V. Chinnadurai and K. Arulmozhi

In this paper, we introduce the concept of interval valued fuzzy ideals of Г-near-rings, We also characterize some of its properties and illustrate with examples of interval valued fuzzy ideals of Г-near-rings .

325-336

Authors: Swamy, N. D. Soner and Ahmed Md. Naji

The k-distance neighborhood polynomial (Nk-polynomial) of a graph G is the ordinary generating function for the number of k-distance neighborhood of the vertices of G and defined as Nk(G; x) = diaΣm(G)k=0 (Σn i=1 dk(vi))k; where diam(G) is the diameter of G and dk(v) = jfu 2 V (G) : d(v; u) = kgj. In this paper, we establish the exact formulas of the Nk-polynomial for a splitting graph S(G) of a graph G. The Nk-polynomials of some well-known graphs as complete Kn, path Pn, cycle Cn, complete bipartite Kr;s and star K1;n are presented.

345-355

Authors: Said Beloul and Arslan Hojet Ansari

The aim of this paper is to prove some common fixed point theorems for two weakly subsequentially continuous and compatible of type (E) pairs of self mappings in Menger spaces, two examples are given to illustrate our results.

365-367

Authors: Yogesh J. Bagul

In this note, natural exponential bounds for coshx are established. The inequalities thus obtained are interesting and sharp.

385-389

Authors: Marapureddy Murali Krishna Rao

In this paper, we introduce the notion of a left zeroid and a right zeroid elements of semirings. We prove that a left zeroid  of a simple semiring M is regular if and only if M is a regular semiring and studied some of their properties.

397-400

Authors: Zongtian Wei and Yinkui Li

In this note, we point out some mistakes in Kurkcu and Aksan (2016, [2]). We also give the correct definition of neighbor-toughness. Finally,some examples, comments and generalized results related to the computation of the parameter are presented.

11-19

Authors: K. Pattabiraman and P. Kandan

The weighted Szeged index of a connected graph G is defined as Szw(G) = Σ e=uv 2E(G) ( dG(u) + dG(v))nGu (e) nGv (e); where nGu (e) is the number of vertices of G whose distance to the vertex u is less than the distance to the vertex v in G: In this paper, we have obtained the weighted Szeged index Szw(G) of the splice graph S(G1;G2; y; z) and link graph L(G1;G2; y; z).

37-43

Authors: M. Murali Krishna Rao and B. Venkateswarlu

In this paper, we introduce the notion of zero divisors free G-semiring. we study the properties of zero divisors free G-semiring and characterize the zero divisors free G-semiring.

55-66

Authors: K. Srinivasa Rao, R. Murali and S. K. Rajendra

Let G be a nontrivial connected graph on which is dened a coloring c : E(G) ! f1; 2;


; kg; k 2 N, of the edges of G, where adjacent edges may be colored the same. A path in G is called a rainbow path if no two edges of it are colored the same. G is rainbow connected if G contains a rainbow u

81-88

Authors: Nilanjan De

In this study, the explicit expressions for F-index and coindex of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph (line graph of the subdivision graph) are obtained.

99-112

Authors: G.Mohanraj and E.Prabu

In this paper, we establish that the fuzzy sum of two (; )-fuzzy right [left] ideals of hemirings R is again a (; )-fuzzy right [left] ideal of R: It fails for two (; )-fuzzy right [left] h-ideals of R: Moreover, we investigate that the fuzzy h-sum of two (; )-fuzzy right [left] ideals is a (; )-fuzzy right [left] h-ideal of R. We explore that the fuzzy h-intrinsic product of two (; )-fuzzy right [left] ideals of R is a (; )-fuzzy right [left] h-ideal of R: Further we investigate that the fuzzy h-intrinsic product of (; )-fuzzy left and (; )-fuzzy right ideals of R is a (; )-fuzzy h-ideal of R:

123-133

Authors: Mohammad Munir and Anum Shafiq

Bi ideals are the generalization of quasi ideals which are themselves the generalization of the so called one-sided, right and left ideals. In this paper, we dene the m-bi ideals as a generalization of the bi ideals. The important properties of the m-bi ideals from the pure algebraic point of view have been described. Moreover, we present the form of the m-bi ideals generated by subsets of the semiring. On the basis of these properties, further characterizations of the semiring will be helpful.

145-154

Authors: B. Fidan and S. Dirik

In this paper, we study the geometry of the contact pseudo-slant submanifolds of a cosymplectic manifold. Necessary and sufficient conditions are given for a submanifold to be a contact pseudo-slant submanifold, contact pseudo-slant product, mixed totally geodesic, D and D?- totally geodesic in a cosymplectic manifold .In this paper, we study the geometry of the contact pseudo-slant submanifolds of a cosymplectic manifold. Necessary and sufficient conditions are given for a submanifold to be a contact pseudo-slant submanifold, contact pseudo-slant product, mixed totally geodesic, D and D?- totally geodesic in a cosymplectic manifold .

161-168

Authors: Girish V R and P. Usha

A set of vertices S is said to dominate the graph G if for each v =2 S, there is a vertex u 2 S with u adjacent to v. The minimum cardinality of any dominating set is called the domination number of the graph G and is denoted by (G). A dominating set D of a graph G = (V;E) is a nonsplit dominating set if the induced graph hV

177-188

Authors: Daniel Abraham Romano

In this paper, basing our consideration on the sets with the apartness relation, we analyze characteristics of some special relations to these sets such as co-order and co-quasiorder and coequality relations. In addition, we analyze two special classes of subsets, co-filters and co-ideals, of ordered set under a co-quasiorder relation. This investigation is into the Bishop's Constructive mathematics.

407-415

Authors: Derya Dogan Durgan and Ferhan Nihan Altundag

A set D  V (G) of a graph G = (V;E) is a liar's dominating set if (1) for all v 2 V (G) jN[v] \ Dj  2 and (2) for every pair u; v 2 V (G)of distinct vertices, jN[u] [ N[v] \ Dj  3. In this paper, we consider the liar's domination number of some middle graphs. Every triple dominating set is a liar's dominating set and every liar's dominating set must be a double dominating set. So, the liar's dominating set lies between double dominating set and triple dominating set.

427--435

Authors: O. Nethaji, I. Rajasekaran and O. Ravi

In this paper, another generalized class of tau⋆ called mildly Ig-omega-closed sets is introduced and the notion of mildly Ig-omega-open sets in ideal topological spaces is introduced and studied. The relationships of mildly Ig-omega-closed sets with various other sets are investigated.

445-450

Authors: K. Angaleeswaria and V. Swaminathan

Let G be a finite simple undirected graph. G is said to be a well covered graph if every maximal independent set is a maximum independent set. A graph is weakly well covered if every non-maximal independent set is contained in a maximum independent set. In an earlier paper, some results on weakly well covered graphs are derived. In this paper, a study of weakly well covered nature of G [ H, G + H, G  H, GH, G  H is made when G and H are weakly well covered graphs.

465-472

Authors: Dusko Jojic

All dissections of a convex (mn + 2)-gons into (m + 2)-gons are facets of a simplicial complex. This complex is introduced by S. Fomin and A.V. Zelevinsky in [7]. We reprove the result of E. Tzanaki about shellability of such complex by finding a concrete shelling order. Also, we use this shelling order to find a combinatorial interpretation of h-vector and to describe the generating facets of these complexes.

479-489

Authors: Ganesan Thangaraj and Raja Palani

In this paper, the concepts of fuzzy sigma-boundary set, fuzzy co-sigma-boundary set, in fuzzy topological spaces are introduced and studied. By means of fuzzy sigma-boundary sets, the concept of fuzzy weakly Baire space is defined and several characterizations of fuzzy weakly Baire spaces are studied.

505-514

Authors: I. Kulrekha Mudartha, R. Sundareswaran and V. Swaminathan

Terasa W. Haynes et. al. [7], introduced the concept of irredundance in graphs. A subset S of V (G) is called an irredundant set of G if for every vertex u 2 S, pn[u; S] ̸= ϕ. The minimum (maximum)cardinality of a maximal irredundant set of G is called the irredundance number of G (upper irredundance number of G) and is denoted by ir(G)(IR(G)). A subset V (G) is called an ir-set if it is an irredundant set of G of cardinality ir(G). A vertex u 2 V (G) is called ir-good if u belongs to an ir-set of G. G is said to be ir-excellent if every vertex of G is ir-good. In this paper, a study of the excellent graphs with respect to irredundance is initiated.

527--538

Authors: G. Mohanraj and E. Prabu

In this paper, we redefine the concepts of (landa; mi)-fuzzy right [left] ideals of hemirings by using the notions of fuzzy sum and fuzzy product. And also the notions of (landa; mi)-fuzzy right [left] h-ideals of hemirings are redefined by fuzzy sum, fuzzy closure and fuzzy product. Further, using the notions of fuzzy h-sum and fuzzy h-product, we characterize (lamda; mi)-fuzzy right [left] h-ideals. In particular, we investigate (landa; mi)-fuzzy right [left] h-ideals by using fuzzy h-sum and fuzzy h-intrinsic product.

549-560

Authors: Seyed Masoud Aghayan, Ahmad Zireh and Ali Ebadian

In this paper, we obtain the existence and the uniqueness of common best proximity point theorems for non-self mappings between two subsets of a complex valued metric space satisfying certain contractive conditions. Our results supported by some examples.

573-580

Authors: A.P. Santhakumaran, P. Titus and K. Ganesamoorthy

For a connected graph G = (V,E) of order at least two, a total detour monophonic set of a graph G is a detour monophonic set S such that the subgraph induced by S has no isolated vertices. The minimum cardinality of a total detour monophonic set of G is the total detour monophonic number of G and is denoted by dmt(G). A subset T of a minimum total detour monophonic set S of G is a forcing total detour monophonic subset for S if S is the unique minimum total detour monophonic set containing T. A forcing total detour monophonic subset for S of minimum cardinality is a minimum forcing total detour monophonic subset of S. The forcing total detour monophonic number ftdm(S) in G is the cardinality of a minimum forcing total detour monophonic subset of S. The forcing total detour monophonic number of G is ftdm(G) = min{ftdm(S)}, where the minimum is taken over all minimum total detour monophonic sets S in G. We determine bounds for it and find the forcing total detour monophonic number of certain classes of graphs. It is shown that for every pair a, b of positive integers with 0 6 a < b and b > 2a+1, there exists a connected graph G such that ftdm(G) = a and dmt(G) = b.

217-229

Authors: K. Pattabiraman and M. Vijayaragavan

In this paper, the edge a-Zagreb Indices and its coindices of some graph operations, such as generalized hierarchical product, Cartesian Product, join, composition of two graphs are obtained. Using the results obtained here, we deduce the F-indices and its coindices for the above graph operation. Finally, we have computed the edge a-Zagreb Index, F-index and their coindices of some important classes of graphs.

243-255

Authors: P. Jeyanthi and K. Jeya Daisy

For any non-trivial abelian group A under addition a graph G is said to be A-magic if there exists a labeling f : E(G) ! A − {0} such that, the vertex labeling f+ defined as f+(v) = Pf(uv) taken over all edges uv incident at v is a constant. An A-magic graph G is said to be Zk-magic graph if the group A is Zk, the group of integers modulo k and these graphs are referred as k-magic graphs. In this paper we prove that the graphs such as open star of shell, flower, double wheel, cylinder, wheel, generalised Petersen, lotus inside a circle and closed helm are Zk-magic graphs. Also we prove that super subdivision of any graph is Zk-magic.

267-268

Authors: K. P. R. Rao and Sk. Sadik

In this paper, we obtain a Pressic type fixed point theorem for three pairs of jointly 3k-weakly compatible maps in D-metric spaces.We also present an example to illustrate our main theorem. We also obtain four corollaries for four maps, three maps,two maps and a single map. We also give some probable modifications of Theorems of [5, 12, 13] in G-metric spaces.

293-303

Authors: Daniel A. Romano

The setting of this article is Classical algebra and Bishop's constructive algebra (the algebra based on the Intuitionistic logic). The Esakia's concept in the classical mathematics of strongly isotone mapping between ordered sets is extended onto two different concepts of mappings: on the concept of weakly isotone and the concept of strongly reverse isotone mapping of relational systems. Some characterizations of those mappings are given and some application of those mappings in ordered semigroup theory are given.

317-325

Authors: G.C. Rao and K. Ravibabu

In this paper, we introduce the concept of permuting tri-f-derivation in an Almost Distributive Lattice (ADL) and derive some important properties of permuting tri-f-derivation in ADLs.

339-352

Authors: G.Nanaji Rao and Terefe Getachew Beyene

The concept of annihilator ideal is introduced in an Almost Semi-lattice (ASL) L with 0. It is proved that the set of all annihilator ideals of an ASL L with 0 forms a complete Boolean algebra. The concept of annihilator preserving homomorphism is introduced in an ASL L with 0. A suficient condition for a homomorphism to be annihilator preserving is derived. Finally, it is proved that the homomorphic image and the inverse image of an annihilator ideal are again annihilator ideals.

363-371

Authors: Rabia Nazir, Muhammad Shoaib Sardar, Sohail Zafar and Zohaib Zahid

We report explicit formulas for the edge version of harmonic index and harmonic polynomial of several classes of bridge graphs.

379-385

Authors: Vecdi Aytac

In a communication network, several vulnerability measures are used to determine the resistance of the network to disruption of operation after the failure of certain stations or communication links. If the communication network is modeled as a simple, undirected, connected and unweighted graph G, then average lower independence number of a graph G can be considered as a measure of graph vulnerability and is dened by iav (G) = 1jV (G)jΣv2V (G) iv(G) where iv(G) is the minimum cardinality of a maximal independent set that contains v. In this paper, I consider the average lower independence number of the thorn graphs of special graphs.

395-401

Authors: M. Senthilkumaran and S. Karthigai Selvam

In this paper, we find exact solitary wave solutions for the variable coefficient KdV Burgers equation of the form ut+uux+f(t)uxx+g(t)uxxx = 0. We construct a transformation of variables which is applied in order to obtain a constant coefficient KdV Burgers equation and also we obtain certain solitary wave solutions with a constraint on f(t) and g(t).