Trees with unique minimum p-dominating sets - Lu, You; Hou, Xinmin; Xu, Jun-Ming; Li, Ning (Utilitas Mathematica, 2011)
Let p be a positive integer and G = (V(G),E(G)) a simple graph. A p-dominating set of G is a subset S of V(G) such that every vertex not in S is dominated by at least p vertices in S. The p-domination number γP(G) is the minimum cardinality among the p-dominating sets of G. In this paper, for p ≥ 2, we give three equivalent conditions for trees with unique minimum p-dominating sets and also give a constructive characterization of such trees.