Some product graphs with power dominating number at most 2

Let S be a set of vertices of a graph G. Let M[S] be the set of vertices built from the closed neighborhood N[S] of S, by iteratively applying the following propagation rule: if a vertex and all but exactly one of its neighbors are in M[S], then the remaining neighbor is also in M[S]. A set S is called a power dominating set of G if M[S]=V(G). The power domination number ¿P(G) 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 1=¿P(G*H)=2 for product graphs.Postprint (published version