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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.
Antony et al. (Thu,) studied this question.