On self-clique graphs with triangular cliques

Abstract

A graph is an {r,s}-graph if the set of degrees of their vertices is {r,s}. A clique of a graph is a maximal complete subgraph. The clique graphK(G) of a graph G is the intersection graph of all its cliques. A graph G is self-clique if G is isomorphic to K(G). We show the existence of self-clique {5,6}-graphs whose cliques are all triangles, thus solving a problem posed by Chia and Ong (2012).