Paired domination integrity of derived graphs of cycles

Abstract

The study of the vulnerability of real-life networks helps network designers construct networks such that their stability is maintained even under the disruption of a few nodes or links connecting the nodes. In this paper, we study the vulnerability of larger networks through a vulnerability parameter called paired domination integrity. The paired domination integrity of a graph G is defined as the minimum value of the sum of the cardinality of a paired dominating set S of G and the order of the largest component in < V (G)−S >. The minimum is taken over all possible paired dominating sets. The above-mentioned large networks are modelled by some derived graphs of Cn, such as the Middle, Total, Central, and Mycielskian graphs.