Domination and Bondage Number for Double Vertex Graphs of Some Graphs

Abstract

If a network modeled by a graph, then there are various graph theoretical parameters used to express the vulnerability and stability of communication networks. One of them is the concept of bondage number  based on domination. The dominating set of a graph is a vertex set in that  every vertex which is not in the dominating set is adjacent to at least one vertex of the dominating set. The domination number is the minimal cardinality  among  all dominating sets. The bondage number of any graph is the minimal cardinality among all sets of edges whose removal from the graph results in a graph with domination number greater than the domination number of the preliminary graph. In this paper, we investigate the domination and bondage numbers for double vertex graphs of some certain graphs.