International Journal of Mathematics and Soft Computing

9-14

Authors: S.V Padmavathi, V Swaminathan

Let $G$ be a simple connected graph. A subset $S$ of vertices of $G$ is said to be a convex set if for any two vertices $u$, $v$ of $S$, $S$ contains all the vertices of every $u - v$ shortest path in $G$. The convexity number $con(G)$ of $G$ is the maximum cardinality of a proper convex set of $G$. The local convexity number of a graph denoted by $l_{1}con(G)$ is defined as the maximum of $\{con(< N[x]>) / x \in V(G) $ and $ con(< N[x]>) $ set is a proper convex set of $G \}$. For a connected graph $G$ of order $n \geq 3$, we have $2 \leq l_{1}con(G) \leq n-1$. Local convex set for which its cardinality is same as $l_{1}con(G)$ is called a maximum local convex set. Local clique number denoted by $\omega_{1}(G)$ is the cardinality of a maximum clique in the set of all maximum local convex sets of $G$. Here we present characterisation of graphs for which $l_{1}con (G) = con (G)$, equivalent condition in graphs for which $N[S]$ is convex for any connected subgraph $< S >$ of $G$ is presented. Interesting results and construction of graphs with prescribed $l_{1}con(G)$, $\omega_{1}(G)$ are also presented.

21-27

Authors: Neha Bharatbhai Rathod, Kailas Khimjibhai Kanani

In this paper, we discuss 4-cordial labeling of some path related graphs. We prove that middle graph, total graph and splitting graph of the path are 4-cordial. In addition to this we prove that $P_n^2 $and triangular snakes are 4-cordial.

39-49

Authors: S Meena, A Kavitha

A graphG  (V,E) with n vertices is said to admit prime labeling if its vertices can be labeled with distinct positive integers not exceeding n such that the label of each pair of adjacent vertices are relatively prime. A graph G which admits prime labeling is called a prime graph and a graph G is said to be a strongly prime graph if for any vertex v of G there exists a prime labeling f satisfying f v 1. In this paper we prove that the graphs n bk P C , * bk n C C , k n C P , 1 G K where G is a ( ) n n C C graph and splitting graph of 1,n K are strongly prime graphs.

59-68

Authors: P Roushini Leely Pushpam, Suseendran Chitra

Let G = (V,E) be a graph. A dominating set S ⊆ V (G) is an efficient dominating setif S is a 2-packing set. The set S is a secure dominating set of G if for each u ∈ V \S there exists a vertex v ∈ S such that uv belongs to the edge set of G and (S\{v}) ∪ {u} is a dominating set of G. In this paper we introduce efficient secure domination in graphs. We define and study the parameter efficient secure domination number of G.

75-82

Authors: Himaya Jaleela Begum, S Jeyalakshmi

In this paper we introduce the notion of anti fuzzy bi-ideals in near-rings and give some characterizations of anti fuzzy bi-ideals in near-rings.

91-103

Authors: S Ravi Narayanan, N R Santhi Maheswari

In this paper $d_{2}$- degree and total $d_{2}$-degree of a vertex in bipolar fuzzy graphs are defined. Also (2,$c_{1}$,$c_{2}$))-regularity and totally (2,$c_{1}$,$c_{2}$))-regularity of bipolar fuzzy graphs are defined. A relation between (2,($c_{1}$,$c_{2}$))-regularity and totally (2,($c_{1}$,$c_{2}$))-regularity on bipolar fuzzy graph is studied. (2,($c_{1}$,$c_{2}$))-regularity on path on four vertices, a Barbell graph $B_{m,n}$ (n$>$1) and a cycle $C_{n}$ are studied with some specific membership functions.

115-125

Authors: Roushini Leely Pushpam, G Navamani

Eternal 1-secure set of a graph $G = (V, E)$ is defined as a set $S_0 \subseteq V$ that can defend against any sequence of single-vertex attacks by means of single guard shifts along edges of $G$. That is, for any $k$ and any sequence $v_1, v_2, \dots, v_k$ of vertices, there exists a sequence of guards $u_1, u_2, \dots, u_k$ with $u_i \in S_{i-1}$ and either $u_i = v_i$ or $u_iv_i \in E$, such that each set $S_i = (S_{i-1} - \{u_i\}) \cup \{v_i\}$ is dominating. It follows that each $S_i$ can be chosen to be an eternal 1-secure set. The {\it eternal 1-security number}, denoted by $\sigma_1(G)$, is defined as the minimum cardinality of an eternal 1-secure set. The {\it Eternal $m$-security} number $\sigma_m(G)$ is defined as the minimum number of guards to handle an arbitrary sequence of single attacks using multiple-guard shifts. In this paper we characterize the class of trees and split graphs for which $\sigma_m(G) = \gamma(G)$. We also characterize the class of trees, unicyclic graphs and split graphs for which $\sigma_m(G) = \beta(G)$.

135-143

Authors: S K Patel, N N Shrimali

In this paper we introduce neighborhood-prime labeling and investigate neighborhoodprime labelings for paths, cycles, helm, closed helm and flower. Also we establish a sufficient condition for a graph to admit neighborhood-prime labeling.

155-164

Authors: Anandhapandian Poongothai, R Parimelazhagan

The aim of this paper is to introduce some new type of seperation axioms and study some of their basic properties. Some implications between T0, T1 and T2 axioms are also obtained.

173-181

Authors: Hariwan Zikri Ibrahim

The main goal of this paper is to introduce and study new notions of continuity, compactness and stability in ditopological texture spaces based on the notions of b-g-open and b-g-closed sets and some of their characterizations are obtained.

189-195

Authors: K Thirugnanasambandam, K Venkatesan

Let G be a graph with p vertices and q edges. Let be an injective function. For a vertex labeling f, the induced edge labeling is defined by = . f is called a super root square mean if . A graph which admits super root square mean labeling is called super root square mean graph. In this paper, we investigate super root square mean labeling of some graphs.