Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 285
Chromatic identities on maximal triangle-free graphs
Ez-Zobair Bidine, Taoufiq Gadi, Mustapha Kchikech, Olivier Togni
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 29, 2022
March 03, 2247
April 15, 2247

Abstract: A graph is maximal triangle-free if no edge may be added without producing a triangle. A triangle-free graph is maximal triangle-free if and only if its diameter is two. The neighborhood of every vertex in triangle-free graphs is an independent set. Then, in such graphs, it is evident that $\Delta(G) \leq \alpha(G)$, where $\Delta(G)$ and $\alpha(G)$ stand for the maximum degree and the independence number of a graph $G$, respectively. In 1964, Vizing \cite{vizing1964estimate} showed that every graph $G$ has edge-chromatic number $\chi'(G)$ either $\Delta(G)$ (known as Class I graphs) ...