Let $G=(V,E)$ be a simple connected graph. A matching $M$ in a graph $G$ is a collection of edges of $G$ such that no two edges from $M$ share a vertex. A matching $M$ is maximal if it cannot be extended to a larger matching in $G$. The cardinality of any smallest maximal matching in $G$ is the saturation number of $G$ and is denoted by $s(G)$. In this paper we study the saturation numbe...

In this paper, we discuss the induced saturation number. It is a nice generalization of the saturation number that will allow us to consider induced subgraphs. We define the induced saturation number, indsat(n,H), to be the fewest number of gray edges in a trigraph T such that H does not appear in any realization of T , but if a black or white edge of T is flipped to gray then there exists a re...