Saturation (graph theory)

Let $G(V,E)$ be a graph and $M$ a matching in $G$ . A vertex $v\in V(G)$ is said to be saturated by $M$ if there is an edge in $M$ incident to $v$ . A vertex $v\in V(G)$ with no such edge is said to be unsaturated by $M$ . We also say that $M$ saturates $v$ .^[1]