Supercliques in a Graph
A set S ⊆ V (G) of a (simple) undirected graph G is a superclique in G if it is a clique and 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 among the supercliques in G, denoted by ωs(G), is called the superclique number of G. In this paper, we determine the superclique numbers of some graphs including those resulting from some binary operations of graphs. We will also show that the difference of the clique number and the superclique number can be made arbitrarily large.
How to Cite
Copyright (c) 2022 European Journal of Pure and Applied Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.
European Journal of Pure and Applied Mathematics will be Copyright Holder.