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A sufficient condition for self-clique graphs

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Abstract

Abstract

The clique graph K(G) of a graph G is the intersection graph of the cliques of G. If G ≌ K(G) then G is a self-clique graph. We describe a sufficient condition for a graph to be self-clique.

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Cited by (5)

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    Citation Excerpt :

    A connected graph G is clique-disk if and only if B=BK(G) has a part-switching involution that maps every vertex x of B to a neighbour of x. □ The hypotheses in the following result were proved to be sufficient for self-cliqueness by Bondy, Durán, Lin and Szwarcfiter [3]. In fact, the first part of the proof of Theorem 1 in [3] shows, in our language, that G2k is clique-disk:Bondy et al. [3]

1

Partially supported by UBACyT Grant TW82 and PID Conicet Grant 644/98, Argentina.

2

Partially supported by the Conselho Nacional de Desenvolvimento Cientifico e Tecnológico, CNPq, and Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro, FAPERJ, Brasil.

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