On self-clique graphs all of whose cliques have equal size. (English) Zbl 1274.05350

Chia, G. L.; Ong, Poh-Hwa

Ars Comb. 105, 435-449 (2012).

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 \(k=3\).

MSC:

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

Keywords:

maximal clique; clique graph; self-clique graph