A New Upper Bound on the Global Defensive Alliance Number in Trees - Chen, Xue-gang; Shiu, Wai Chee (The Electronic Journal of Combinatorics, 2011)
A global defensive alliance in a graph G=(V,E) is a dominating set S satisfying the condition that for every vertex vS, |N[v]S|≥ |N(v)(V-S)|. In this note, a new upper bound on the global defensive alliance number of a tree is given in terms of its order and the number of support vertices. Moreover, we characterize trees attaining this upper bound.