Independent strong domination number of indu-bala product of graphs

Abstract

A set D⊂ V be the strong dominating set of G if every vertex in V − D is strongly dominated by at least one vertex in D. The strong domination number γ<inf>st</inf>(G) of G is the minimum cardinality of a strong dominating set. The independent strong domination number i<inf>s</inf>(G) of a graph G is the minimum cardinality of a strong dominating set which is independent. In this paper, by means of the degree sequences (DS) of graphs and some graph theoretical methods, we determine the independent strong domination number of Indu-Bala product of simple connected graphs and null graphs.