Bulletin of the International Mathematical Virtual Institute

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).

11-21

Authors: Muhammad Sarwar, Mian Bahadur Zada and Saurabh Manro

In this paper, using the (CLR) and (E:A) properties of the involved pairs, common fixed point results for four and six weakly compatible self-mappings are established in complex valued metric spaces. Our results include some known results as special cases.

31-41

Authors: K. Pattabiraman and M. Vijayaragavan

For a (molecular) graph, the hyper Zagreb index is defined as HM(G) = Σuv2E(G) (dG(u) + dG(v))2 and the hyper Zagreb coindex is defined as HM(G) = Σ uv=2 E(G) (dG(u)+dG(v))2: In this paper, the hyper Zagreb indices and its coindices of edge corona product graph, double graph and Mycielskian graph are obtained.

53-63

Authors: B. Chaluvaraju and V. Chaitra

In this paper, we newly constructed the sign dominating outer (inner) switched graph mio d(G) (mii d(G)) of a graph G = (V;E) and establish their properties. Also we determine number of edges and its relation between mio d(G) and mii d(G) in some special classes of graphs are explored.

73-83

Authors: Akram Alqesmah, Anwar Alwardi and R. Rangarajan

Let G = (V;E) be a connected graph. A subset S of V is called injective dominating set (Inj-dominating set) if for every vertex v 2 V

93-102

Authors: R.D. Jagatap and Y.S. Pawar

In this paper we introduce the concepts of prime, semiprime, strongly prime, irreducible and strongly irreducible bi-ideals in a Г-semiring. Characterizations of a Г-semiring using these concepts are furnished. A topology on the set of strongly prime bi-ideals is defined and a property of the space of strongly prime bi-ideals of a Г-semiring is furnished.

117-128

Authors: Nilanjan De

The Narumi-Katayama index of a graph G is equal to the product of degrees of all the vertices of G. In this paper, we examine the Narumi- Katayama index of some derived graphs such as a Mycielski graph, subdivision graphs, double graph, extended double cover graph, thorn graph, subdivision vertex join and edge join graphs.

139-151

Authors: O. Ravi, P. Sekar and K. Vidhyalakshmi

In this paper, we introduce some generalizations of !-open sets in ideal topological spaces and investigate some properties of the sets. Moreover, we use them to obtain decomposition of continuity via idealization.

165-171

Authors: Adara M. Blaga

In the context of para-Kenmotsu geometry properties of the generalized dual connections of some canonical linear connections (Levi-Civita, para-Kenmotsu canonical, Golab and Zamkovoy canonical paracontact connections) are established.

181-191

Authors: Ahmed A. Abdelhakim and R. A. Rashwan

We prove strong convergence of an implicit iteration procedure equipped with error terms to the solution of a system involving total asymptotically non-expansive mappings, in uniformly convex Banach spaces.