The icosahedron is clique divergent (Q1868854)

A clique of a graph is a maximal complete subgraph. The clique graph \(k(G)\) is the intersection graph of all cliques of \(G\). The iterated clique graph \(k^n(G)\) is the result of repeatedly applying the clique graph operator to \(G\) for \(n\) times. A graph \(G\) is said to be clique divergent if the number of vertices of \(k^n(G)\) approaches infinity as \(n\) goes to infinity. This paper proves the clique divergence of the icosahedron.