Edge contraction and edge removal on iterated clique graphs

The clique graph K(G)K(G) of a graph GG is the intersection graph of all its (maximal) cliques. We explore the effect of operations like edge contraction, edge removal and others on the dynamical behavior of a graph under the iteration of the clique operator KK. As a consequence of this study, we can now prove the clique divergence of graphs for which no previously known technique would yield the result. In particular, we prove that every clique divergent graph is a spanning subgraph of a clique divergent graph with diameter two.