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A defensive alliance in a graph \( G = (V,E) \) is a set of vertices \( S \subseteq V \) satisfying the condition that every vertex \( v \in S \) has at most one more neighbor in \( V – S \) than it has in \( S \). Because of such an alliance, the vertices in \( S \), agreeing to mutually support each other, have the strength of numbers to be able to defend themselves from the vertices in \( V – S \). In this paper, we introduce this new concept, together with a variety of other kinds of alliances, and initiate the study of their mathematical properties.