The Equivalence Chain of a Graph

Let \( G = (V, E) \) be a graph. A subset \( S \) of \( V \) is called an \emph{equivalence set} 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 \emph{equivalence chain} of \( G \). We present several basic results on these parameters and problems for further investigation.