Total colouring of a fuzzy graph  is a proper colouring of vertices and edges. In this paper, we define total colouring of a fuzzy graph using strong α-cuts and find fuzzy chromatic number for both vertex and edge separately and fuzzy total chromatic number of a fuzzy graph with fuzzy numbers through the strong a-cuts. A few results based on strong a-cuts are obtained and an application to traffic light control system is explained.

fuzzy chromatic number, chromatic index, total chromatic number, strong α-cut.

Received: April 5, 2023;  Accepted: May 20, 2023 Published: December 5, 2023

How to cite this article: B. Amala Jasmine, M. Antony Arockiasamy, K. Jency Priya and P. Rajapushpam, Total colouring of fuzzy graphs using strong α-cuts, Advances in Fuzzy Sets and Systems 28(2) (2023), 77-86. http://dx.doi.org/10.17654/0973421X23005

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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