On the domination of the products of graphs II: Trees
Michael S. Jacobson, Lael F. Kinch · Journal of Graph Theory · 1986
Abstract For a graph G, a subset of vertices D is a dominating set if for each vertex X not in D, X is adjacent to at least one vertex of D. The domination number, γ(G), is the order of the smallest such set. An outstanding conjecture in the theory of domination is for any two graph G and H, One result presented in this paper settles this question in the case when at least one of G or H is a tree. We show that for all graphs G and any tree T. Furthermore, we supply a partial characterization for which pairs of trees, T1 and T2, strict inequality occurs. We show for almost all pairs of trees.