Locally C6 graphs are clique divergent

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 k(n)G are defined by k(0)G = G and k(n+1)G = kk(n)G. A graph G is said to be k-divergent if \V(k(n)G)\ tends to infinity with n. A graph is locally, C-6 if the neighbours of any given vertex induce an hexagon. We prove that all locally C-6 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. (C) 2000 Published by Elsevier Science B.V. All rights reserved.