On Self-Clique Graphs all of whose Cliques have Equal Size

Abstract

The clique graph of a graph \(G\) is the graph whose vertex set is the set of cliques of \(G\) and two vertices are adjacent if and only if the corresponding cliques have non-empty intersection. A graph is self-clique if it is isomorphic to its clique graph. In this paper, we present several results on connected self-clique graphs in which each clique has the same size \(k\) for \(k = 2\) and \(k = 3\).