A defensive alliance in a graph G = (V, E) is a set of vertices S subset of V satisfying the condition that, for each nu is an element of S, at least one half of its closed neighbors are in S. A defensive alliance S is called a critical defensive alliance if any vertex is removed from S, then the resulting vertex set is nota defensive alliance any more. An alliances is called global if every vertex in V(G)\S is adjacent to at least one member of the alliance S. In this paper, we shall propose a way for finding a critical global defensive alliance of star graphs. After counting the number of vertices in the critical global defensive alliance, we can derive an upper bound to the size of the minimum global defensive alliances in star graphs. (C) 2009 Elsevier B.V. All rights reserved.
