Locally C6 graphs are clique divergent

F. Larrión, V. Neumann-Lara
2000 Discrete Mathematics  
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 deÿned 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 inÿnity 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 inÿnity with n while the sizes of the cliques remain bounded.
doi:10.1016/s0012-365x(99)00233-2 fatcat:vvjpwiucjjfklf4rdbdrp7v7y4