Bounds on Powerful Alliance Numbers

Abstract

Let \(G = (V, E)\) be a graph. Then \(S \subseteq V\) is an excess-\(t\) global powerful alliance if \(|N[v] \cap S| \geq |N[v] \cap (V – S)| + t\) for every \(v \in V\). If \(t = 0\), this definition reduces to that of a \({global \;powerful \;alliance}\). Here we determine bounds on the cardinalities of such sets \(S\).