Strong restrained domination number on trees and product of graphs: An algorithmic approach

Abstract

A restrained dominating set [Formula: see text] is said to be a strong restrained dominating set of G if every vertex [Formula: see text] is adjacent to a vertex [Formula: see text] and [Formula: see text]. The minimum cardinality of a strong restrained dominating set of G is said to be the strong restrained domination number of [Formula: see text] and it is denoted by [Formula: see text]. We characterize all the trees with [Formula: see text]. We show that if [Formula: see text] is a tree of order [Formula: see text], then [Formula: see text] and characterize the extremal trees by achieving this lower bound. Simulation was carried out for the strong restrained domination number of Cartesian, strong and lexicographic product under four different network topologies and it was noted that [Formula: see text] under these four network topologies. Furthermore, the strong restrained domination number of [Formula: see text] and [Formula: see text] for any [Formula: see text] and [Formula: see text] for any [Formula: see text] is determined.