Eternal Security in Graphs of Fixed Independence Number

Abstract

We show that if the independence number of a graph is $\alpha$, then the eternal security number of the graph is at most $(\genfrac{}{}{0ex}{}{\alpha +1}{2})$, solving a problem stated by Goddard, Hedetniemi, and Hedetniemi $[JCMCC,\text{ vol. }52,\text{ pp. }160-180]$.