Clique divergent graphs with unbounded sequence of diameters (Q1292855)

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 \(k^nG\) are defined by \(k^0G= G\) and \(k^{n+1}G= kk^nG\). A graph \(G\) is said to be \(k\)-divergent if the order of \(k^nG\) tends to infinity with \(n\). The authors 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 the chromatic numbers remain bounded.