The Equivalence Chain of a Graph

Abstract

Let $G=(V,E)$ be a graph. A subset $S$ of $V$ is called an $equivalenceset$ if every component of the induced subgraph $(S)$ is complete. In this paper, starting with the concept of equivalence set as a seed property, we form an inequality chain of six parameters, which we call the $equivalencechain$ of $G$. We present several basic results on these parameters and problems for further investigation.