PAIRED DOMINATION INTEGRITY OF DERIVED GRAPHS OF CYCLES

PAIRED DOMINATION INTEGRITY OF DERIVED GRAPHS OF CYCLES

A. C. Antony , V. Sangeetha

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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.

Keywords

Domination integrity, Middle graph, Total graph, Central graph, Mycielskian graph.