Bulletin of the International Mathematical Virtual Institute

1-9

Authors: Hakeem A. Othman

In this paper, new classes of sets in general topology called a supra-beta-open (closed) (an infra-beta-open (closed)) set are introduced. Using new concepts, the fundamental properties and special results are highlighted. The relations between supra-beta-open (closed)(an infra-beta-open (closed)) set and other topological sets are investigated. Moreover, counter-examples are given to show that the converse of these relations in Diagram 1 need not be true, in general. Finally, some special theorems are introduced by adding condition to achieve the converse relations in Diagram 1.

23-30

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

A set S of vertices of a connected graph G is a monophonic set if every vertex of G lies on an x−y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is the monophonic number of G, denoted by m(G). A set S of vertices of a graph G is an edge monophonic set if every edge of G lies on an x − y monophonic path for some elements x and y in S. The minimum cardinality of an edge monophonic set of G is the edge monophonic number of G, denoted by em(G). A set S of vertices of a graph G is a restrained edge monophonic set if either V = S or S is an edge monophonic set with the subgraph G[V −S] induced by V −S has no isolated vertices. The minimum cardinality of a restrained edge monophonic set of G is the restrained edge monophonic number of G and is denoted by emr(G). It is proved that, for the integers a, b and c with 3 6 a 6 b < c, there exists a connected graph G having the monophonic number a, the edge monophonic number b and the restrained edge monophonic number c.

43-52

Authors: P. Sundarayya, Ramesh Sirisetti and V. Sriramani

In this paper, we recall two partial orderings on a C-algebra. Two types of decompositions are derived by using these partial orderings, which are not dual to each other. Two sufficient conditions for a C-algebra to become a Boolean algebra in terms of C-algebras La, Ra are obtained.

65-72

Authors: Rajinder Sharma

In this paper , we established some common fixed point theorems for two pairs of self maps by using the more weaker notion of weak sub sequential continuity (wsc) with compatibility of type (E) in non Archimedean Menger PM space. We improve some earlier results in this line.

85-92

Authors: Valeriu Popa and Alina-Mihaela Patriciu

The purpose of this paper is to prove a general fixed point theorem for two pairs of mappings satisfying implicit relations in orbitally 0 - complete partial metric space, which include also a result of Hardy - Rogers type.

103-116

Authors: D. R. Prince Williams

In this paper, we introduce a notion of fuzzy n-ary subgroups with respect to t-conorm(s-fuzzy n-ary subgroups) in an n-ary groups (G; f) and have studied their related properties. The main contribution of this paper are studying the properties of s-fuzzy n-ary subgroups over s-level n-ary subgroup of (G; f) , n-ary homomorphism and reta(G; f). Moreover some results of the S-product of s-fuzzy n-ary relations in an n-ary groups (G; f) are also obtained.

129-138

Authors: Pramod Kumar Pandey

In this article we have considered general third order boundary value problems and proposed an efficient difference method for numerical solution of the problems. We have shown under appropriate conditions that proposed method is convergent and second order accurate. The numerical results in experiment on test problems show the simplicity and efficiency of the method.

153-164

Authors: Debabrata Mandal

The purpose of this paper is to introduced neutrosophic hyperideals of a Г-semihyperring and consider some operations on them to investigate some of its basic properties.

173-179

Authors: B. Basavanagoud, Veena R. Desai and Shreekant Patil

The first, second and modified first multiplicative Zagreb indices of a graph $G$ are defined, respectively, as $\prod_{1}(G)$ = $\prod \limits_{u\in V(G)}d_{G}(u)^2$, $\prod_{2}(G)$ = $\prod \limits_{uv\in E(G)}d_{G}(u)d_{G}(v)$ and $\prod_{1}^{*}(G)$ = $\prod \limits_{uv\in E(G)}[d_{G}(u)+d_{G}(v)]$ where $d_{G}(w)$\ is the degree of vertex $w$ in $G$. In the present study, we obtain the expressions for $\prod_{1}$, $\prod_{2}$ and $\prod_{1}^{*}$ of generalized transformation graphs $G^{ab}$.

193-202

Authors: K. Pattabiraman

In this paper, we present the various upper and lower bounds for the product version of reciprocal degree distance in terms of other graph inavriants. Finally, we obtain the upper bounds for the product version of reciprocal degree distance of the composition, Cartesian product and double of a graph in terms of other graph invariants including the Harary index and Zagreb indices.