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Convergence of iterated clique graphs. (English) Zbl 0766.05096
Let \(C(G)\) be the clique graph of a graph \(G\), and let \(C^ n(G)=C(C^{n-1}(G))\). The graph \(G\) is said to be clique-convergent to a set \(M=\{F,C(F),C^ 2(F),\dots,C^{p-1}(F)\}\) of graphs if \(C^ p(F)=F\) and \(C^ m(G)=F\) for some integer \(m\). Necessary conditions for a graph \(G\) to be clique-convergent are given in terms of simplicial complexes associated with \(G\) and \(F\). For some special classes of clique-convergent graphs the corresponding set \(M\) is determined exactly.

MSC:
05C99 Graph theory
05C65 Hypergraphs
05C10 Planar graphs; geometric and topological aspects of graph theory
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