Cliques and Supercliques in Graphs
Keywords:clique, clique number, superclique, superclique number
A set S ⊆ V (G) of an undirected graph G is a clique if every two distinct vertices in S are adjacent. A clique is a superclique if for every pair of distinct vertices v, w ∈ S, there exists u ∈ V (G) \ S such that u ∈ NG(v) \ NG(w) or u ∈ NG(w) \ NG(v). The maximum cardinality of a clique (resp. superclique) in G is called the clique (resp. superclique) number of G. In this paper, we determine the clique and superclique numbers of some graphs.
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