2021/06/25 by Shahbaznejad, Najibeh, Kazemi, Adel P, Pelayo, Ignacio M
#05C35 #05C69 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2106.13496
Let G be a graph with the vertex set V(G) and S be a subset of V(G) . Let cl(S) be the set of vertices built from S, by iteratively applying the following propagation rule: if a vertex and all of its neighbors except one of them are in cl(S) , then the exceptional neighbor is also in cl(S) . A set S is called a zero forcing set of G if cl(S)=V(G). The zero forcing number Z(G) of G is the minimum cardinality of a zero forcing set. Let cl(N[S]) be the set of vertices built from the closed neighborhood N[S] of S, by iteratively applying the previous propagation rule. A set S is called a power dominating set of G if cl(N[S])=V(G). The power domination number γp (G) of G is the minimum cardinality of a power dominating set. In this paper, we present some families of graphs that their power domination number is 1 or 2.