Some product graphs with power dominating number at most 2

Abstract

Let S be a set of vertices of a graph G. Let be the set of vertices built from the closed neighborhood of S, by iteratively applying the following propagation rule: if a vertex and all but exactly one of its neighbors are in then the remaining neighbor is also in A set S is called a power dominating set of G if The power domination number of G is the minimum cardinality of a power dominating set. In this paper, we present some necessary conditions for two graphs G and H to satisfy for product graphs.