Application of Co-Secure Domination in Sierpinski Networks

Abstract

Security control is crucial in protecting a network from natural and human-made disasters. The theory of graph domination and its variants play a significant role in identifying the sensitive locations in a network where mobile guards have to be placed to protect the network nodes from the risk of attack. To ensure the network’s security, the physically weak or the attacked mobile guard at the node is to be replaced immediately by another guard so that the consequent set of guards continues to protect the network. The set of such nodes thus formed is a co-secure dominating set of the network, and least cardinality of the co-secure dominating set is the co-secure domination number. This article determines a tight bound for the co-secure domination number on the Generalized Sierpinski cycle graphs and Generalized Sierpinski complete graphs.