Global forcing number for maximal matchings in corona products

Abstract

A global forcing set for maximal matchings of a graph $G=(V(G),E(G))$ is a set $S\subseteq E(G)$ such that $M_1\cap S\ne M_2\cap S$ for each pair of maximal matchings $M_1$ and $M_2$ of $G$. The smallest such set is called a minimum global forcing set, its size being the global forcing number for maximal matchings ${\varphi }_{gm}(G)$ of $G$. In this paper, we establish lower and upper bounds on the forcing number for maximal matchings of the corona product of graphs. We also introduce an integer linear programming model for computing the forcing number for maximal matchings of graphs.