Domination Value in P_2□P_n and P_2□C_n

摘要

A set D ⊂ V{G) is a dominating set of a graph G if every vertex of G not in D is adjacent to at least one vertex in D. A minimum dominating set of G, also called a γ(G)-set, is a dominating set of G of minimum cardinality. For each vertex ν∈ V(G), we define the domination value of v to be the number of γ(G)-sets to which v belongs. In this paper, we find the total number of minimum dominating sets and characterize the domination values for P_2□P_n and P_2□C_n.