Global forcing number for maximal matchings in corona products

TL;DR

This paper investigates the global forcing number for maximal matchings in graphs, providing bounds for corona products and introducing an ILP model for computation.

Contribution

It establishes bounds on the forcing number for corona product graphs and proposes an ILP model for calculating this parameter.

Findings

Derived lower and upper bounds for corona product graphs.

Introduced an ILP model for computing the forcing number.

Enhanced understanding of maximal matchings in complex graph structures.

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 $M_1\cap S \neq M_2 \cap S$ 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 $\phi_{gm}(G)$ 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.