Smallest Maximal Matchings of Graphs

Let $G=(V_G, E_G)$ be a simple and connected graph. A set $M\subseteq E_G$ is called matching of $G$ if no two edges $M$ are adjacent. The number in its size. maximal it cannot extended to larger $G$. smallest size the saturation In this paper we concerned with numbers lexicographic product graphs. We also address solve an open problem about maximum matchings graphs given degree $\Delta$.