Bulletin of the International Mathematical Virtual Institute

135-141

Authors: Omur Kivanc Kurkcu and Huseyin Aksan

The vulnerability shows the resistance of the network until com- munication breakdown after the disruption of certain stations or communi- cation links. This study introduces a new vulnerability parameter, neighbor toughness. The neighbor toughness of a graph G is dened as NT(G) = minf jSj !(G=S) : !(G=S) > 1g, where S is any vertex subversion strategy of G and !(G=S) is the number of connected components in the graph G=S. In this paper, the relations between neighbor toughness and other parameters are determined and the neighbor toughness of some specic graphs are obtained.

157-167

Authors: M. Kamal Kumar, R. Murali and V. Chidanandan

Domination and other related concepts in undirected graphs are well studied. Although domination and related topics are extensively studied, the respective analogies on digraphs have not received much attention. Such studies in the directed graphs have applications in game theory and other areas. A directed graph D is a pair (V;E), where V is a non empty set and E is a set of ordered pairs of elements taken from set V . V is called vertices and E set called directed edges. Let D = (V;E) be a digraph if (x; y) 2 E then arc is directed from x to y and is denoted by x ! y. The vertex x is called a predecessor of y and y is called a successor of x. A set S  V of a digraph D is said to be a dominating set of D if 8v =2 S, v is a successor of some vertex s 2 S. In this paper we study domination theory on few well known classes of directed trees. Directed trees are extensively used in path algorithm, scheduling problems, data processing networks, data compression, causal structures like family tree, Bayesian network, moral graphs, in uence diagram etc. The concept of dominating function plays a signicant role in these models.

181-188

Authors: Pankaj Kumar Jhade, R.A.Rashvan and A.S.Saluja

The aim of this paper is to prove a coincidence point theorem for a class of self mappings satisfying nonexpansive type condition under various conditions and a xed point theorem is also obtained. Our results extend and generalizes the corresponding result of Singh et al. [7].

199-208

Authors: Adesanmi Alao Mogbademu

In this paper, we prove some strong convergence theorems of the modified Mann iteration with errors for a new class of nonlinear mappings in real Banach spaces. Our results not only employ a simple proof technique, but also extend some well known results in this area of research.

219-226

Authors: Aleksandr Tsarev, Tongsuo Wu and Artem Lopatin

Let $\tau$ be a subgroup functor (in Skiba's sense) such that all subgroups of any finite group $G$ contained in $\tau(G)$ are subnormal in $G$. In this paper, we show first that the lattice of all $\tau$-closed $n$-multiply composition formations of finite groups $\mathcal C_n^\tau$ is not distributive for every non-negative integer $n$. Next, we prove that if $\mathfrak F \neq (1)$ is a non-empty $\tau$-closed $n$-multiply composition formation then its $\tau$-closed Frattini subformation $\Phi_n^\tau(\mathfrak F)$ consists of all $\mathcal C_n^\tau$-non-generating groups of $\mathfrak F$. Moreover, if $\mathfrak F_1$ is a $\tau$-closed $n$-multiple composition subformation of $\mathfrak F$ then $\Phi_n^\tau(\mathfrak F_1) \subseteq \Phi_n^\tau(\mathfrak F)$.

241-249

Authors: K. M. Nagaraja, P. Siva Kota Reddy and K. Sridevi

Convexity/Concavity nature of different means are generally dis-cussed. But in this paper relative study of convexity/Concavity between different means are found and these results are interpreted in Van der Monde determinants.

259-267

Authors: Daniel A. Romano

This investigation is in the Bishop's constructive mathematics. We discuss about co-order, co-quasiorder and coequality relations on set X with appartness. A connection between the family of all co-quasiorder relations and the family of all coequality relations on set X is given. In addition, a connection between the family of all co-quasiorder relations included in the co-order  and the family of all regular coequality relation on X with respect to  is also given.

13-24

Authors: Anwar Alwardi and P.M.Shivaswamy

Graph polynomials are polynomials associated to graphs that en-code the number of subgraphs with given properties. In this paper we introduce a new type of graph polynomial called neighbourhood polynomial. We obtained the neighbourhood polynomial of some interested standard graphs like complete graph, complete bipartite graph, bi-star graph, spider, wounded spider graph and for some corona product graphs.

37-48

Authors: Harina O. L. Monim, Indah E. Wijayanti and Sri Wahyuni

In the framework of fuzzy sets and corresponding techniques, we investigate functions from a nonempty set X into an ordered structure (S;6) where S is a meet-semilattice.Each function mi : X ! S determines a family of subsets of X, which are called cut sets. Vice versa, particular family of subsets of X, indexed by the elements of S uniquely determines a function from X to S. Further, any function  : X ! S determines a semi-closure operator on S, which induces an equivalence relation on the semilattice S. Using the above results, we classify functions in SX.

55-64

Authors: Saadet Eskiizmirliler, Goksen Bacak-Turan and Refet Polat

A vertex subversion strategy of a graph G, say S, is a set of vertices in G whose closed neighborhood is removed from G. The survival subgraph is denoted by G=S. The neighbor rupture degree of G is dened to be Nr(G) = maxfw(G=S)

77-87

Authors: Fuad S. Al Sarari and S. Latha

In this note, the concepts of (j; i)-symmetric points, Janowski functions and the conic regions are combined to define a class of functions in a new interesting domain which represents the conic type regions. Certain interesting coeficient inequalities are deduced.

97-104

Authors: Tabitha Agnes M., L. Sudershan Reddy, Joseph Varghese K., and John Stephen Mangam

The diametral path of a graph is the shortest path between two vertices which has length equal to diameter of that graph. Diametral path decomposition is introduced as a collection of edge-disjoint diametral paths of a graph so that every edge of the graph appears in exactly one diametral path. Diametral path decomposition number de is the cardinality of such a collection. The diametral path decomposition index De is the number of such decompositions. In this paper, results on de and De in some classes of graphs are presented. Also graphs which admit diametral path decomposition are charecterized.

115-125

Authors: K.P.R.Rao, Sk. Sadik and S.Manro

In this paper, we obtain a unique common fixed point theorem for four self maps satisfying rational ( ; ϕ; φ)-contractive condition using - admissible function in ordered partial metric spaces. Also we give an example to illustrate our main theorem.