Paired Domination Integrity of Graphs

Abstract

The concept of vulnerability in a communication network plays an important role when there is a disruption in the network. There exist several graph parameters that measure the vulnerability of a communication network. Domination integrity is one of the vulnerability parameters that measure the performance of a communication network. In this paper, we introduce the concept of paired domination integrity of a graph as a new measure of graph vulnerability. Let [Formula: see text] be a simple, connected graph. A set of vertices in a graph [Formula: see text], say [Formula: see text], is a paired dominating set if the following two conditions are satisfied: (i) every vertex of [Formula: see text] has a neighbor in [Formula: see text] and (ii) the subgraph induced by [Formula: see text] contains a perfect matching. The paired domination integrity of [Formula: see text], denoted by [Formula: see text], is defined as [Formula: see text], where [Formula: see text] is the order of the largest component in the induced subgraph of [Formula: see text]. In this paper, we determine few bounds relating paired domination integrity with other graph parameters and the paired domination integrity of some classes of graphs.