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{\bf Xue-gang Chen and Wai Chee Shiu}
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{\bf A New Upper Bound on the Global Defensive Alliance Number in Trees}
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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.

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