On a Conjecture about the Saturation Number of Corona Product of Graphs

Abstract

Let $G=\left(V_G,E_G\right)$ be a simple and connected graph. A set $M\subseteq E_G$ is called a matching if no two edges of $M$ have a common endpoint. A matching $M$ is maximal if it cannot be extended to a larger matching in $G$ . The smallest size of a maximal matching is called the saturation number of $G$ . In this paper, we confirm a conjecture of Alikhani and Soltani about the saturation number of corona product of graphs. We also present the exact value of $s\left(G\circ H\right)$ where $H$ is a randomly matchable graph.