The icosahedron is clique divergent

Authors:
Miguel A. Pizaña
Affiliations:
Depto. de Ingeniería Eléctrica, Universidad Autónoma Metropolitana, Av. Michoacán y Purísima s/n, Col. Vicentina, México 09340 DF, Mexico
Venue:
Discrete Mathematics
Year:
2003

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Abstract

A clique of a graph G is a maximal complete subgraph. The clique graph k(G) is the intersection graph of the set of all cliques of G. The iterated clique graphs are defined recursively by k0(G) = G and kn+1(G) = k(kn(G)). A graph G is said to be clique divergent (or k-divergent) if limn → ∞ |V(kn(G))| = ∞. The problem of deciding whether the icosahedron is clique divergent or not was (implicitly) stated Neumann-Lara in 1981 and then cited by Neumann-Lara in 1991 and Larrión and Neumann-Lara in 2000. This paper proves the clique divergence of the icosahedron among other results of general interest in clique divergence theory.