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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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##### References:
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