Graph Theory for Computer Science

11Secure Equitability in Chemical Networks

Annie Alex* and V. Sangeetha

Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, Karnataka, India

Abstract

Let G = (V, E) be a simple connected graph with a set of nodes V(G) and a set of edges E(G). A secure equitable dominating set S ⊆ V(G) is a dominating set in which, for any vertex v ∈ V(G) \ S, there exists at least one vertex u ∈ S such that the vertex u belongs to the equitable neighborhood of v and, if we swap the vertices u and v, then the equitable domination property of the graph does not change. A secure equitable dominating set of minimum number of nodes in G is named a γ^se -set and the cardinality of a γ^se -set is called the secure equitable domination number of G, denoted by (G). In this paper, we study the bounds of secure equitable domination number in certain chemical structures. Moreover, we give an application of the parameter on interconnection networks.

Keywords: Secure equitable domination, chemical networks, silicate, benzoid

11.1 Introduction

Chemical graph theory is one of the rapidly flourishing areas of graph theory. In chemical graph theory, graph-theoretic concepts are used for modeling chemical structures and phenomena. The atoms in any molecular structure can be represented using dots or circles. The chemical bond between two atoms is represented by lines that connect the corresponding ...