Locally C6 graphs are clique divergent 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 knG are defined by k0G=G and kn+1G=kknG. A graph G is said to be k-divergent if V(knG) tends to infinity with n. A graph is locally C6 if the neighbours of any given vertex induce an hexagon. We prove that all locally C6 graphs are k-divergent and that the diameters of the iterated clique graphs also tend to infinity with n while the sizes of the cliques remain bounded.