On Vulnerability Of The Hexagonal Cactus Chains

Abstract

Let G(V(G),E(G)) be a simple molecular graph without directed and multiple edges and without loops. The vulnerability value of a graph shows the resistance of the network after the disruption of some centers or connection lines until a communication breakdown. The domination number and its variations are the most important vulnerability parameters for graphs. One of them is the average lower domination number. It is denoted by , also is defined as: , where the lower domination number , denoted by , is the minimum cardinality of a dominating set of the graph G that contains the vertex v  (Henning 2004). In this paper, the average lower domination number of different hexagonal cactus chains are determined.