Graph relations, clique divergence and surface triangulations

This work has two aims: First, we introduce a powerful technique for proving clique divergence when the graph satisfies a certain symmetry condition. Second, we prove that each closed surface admits a clique divergent triangulation. By definition, a graph is clique divergent if the orders of its iterated clique graphs tend to infinity, and the clique graph of a graph is the intersection graph of its maximal complete subgraphs.