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.