On a graph isomorphic to its intersection graph: self-graphoidal graphs

Abstract

A graph \(G\) is called a graphoidal graph if there exists a graph \(H\) and a graphoidal cover \(\psi\) of \(H\) such that \(G\cong\Omega(H,\psi)\). Then the graph \(G\) is said to be self-graphoidal if it is isomorphic to one of its graphoidal graphs. In this paper, we have examined the existence of a few self-graphoidal graphs from path length sequence of a graphoidal cover and obtained new results on self-graphoidal graphs.