(untitled) (European Journal of Pure and Applied Mathematics, 2023)
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.