Supercliques in a Graph
DOI:
https://doi.org/10.29020/nybg.ejpam.v15i3.4480Abstract
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.
Downloads
Published
Issue
Section
License
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 European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.
By agreeing to this statement, you acknowledge that:
- You retain full copyright over your work.
- The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
- This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.