PAIRED DOMINATION INTEGRITY OF DERIVED GRAPHS OF CYCLES

Year 2025, Volume: 15 Issue: 10, 2453 - 2464, 01.10.2025

Annie Clare Antony Sangeetha Shathish

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 $C_n$, such as the Middle, Total, Central, and Mycielskian graphs.

Keywords

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

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