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On self-clique graphs all of whose cliques have equal size. (English) Zbl 1274.05350
Summary: The clique graph of a graph \(G\) is the graph whose vertex set is the set of maximal cliques of \(G\) and two vertices are adjacent if and only if the corresponding cliques have non-empty intersection. A graph is self-clique if it is isomorphic to its clique graph. In this paper we present several results on connected self-clique graphs in which each clique has the same size \(k\) for \(k=1\) and \(k=3\).

05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C35 Extremal problems in graph theory