A new upper bound on the global defensive alliance number in trees (Q640466)

Summary: A global defensive alliance in a graph \(G = (V, E)\) is a dominating set \(S\) satisfying the condition that for every vertex \(v \in S\), \(|N [v] \cap S| \geq |N (v) \cap (V - S)|\). 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.