Clique divergent graphs with unbounded sequence of diameters Original Research Article

The clique graph kG of a graph G is the intersection graph of the family of all maximal complete subgraphs of G. The iterated clique graphs kn G are defined by k0G = G and kn+1G = kknG. A graph G is said to be k-divergent if |V(kn G)| tends to infinity with n. We provide examples of k-divergent graphs such that the diameters of the iterated clique graphs also tend to infinity with n. Furthermore, the sizes of the cliques and even the chromatic numbers remain bounded.