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 $|N[v]\cap S|\ge |N[v]\cap (V–S)|+t$ for every $v\in V$. If $t=0$, this definition reduces to that of a $globalpowerfulalliance$. Here we determine bounds on the cardinalities of such sets $S$.