Title: Types of fuzzy graph colouring and polynomial ideal theory

Authors: Arindam Dey; Anita Pal

Addresses: Department of Computer Science and Engineering, Saroj Mohan Institute of Technology, Hooghly, India ' Department of Mathematics, National Institute of Technology, Durgapur, India

Abstract: The graph colouring problem (GCP) is one of the most important optimisation problems in graph theory. In real life scenarios, many applications of graph colouring are fuzzy in nature. Fuzzy set and fuzzy graph can manage the uncertainty, associated with the information of a problem, where conventional mathematical models/graph may fail to reveal satisfactory result. To include those fuzzy properties in solving those types of problems, we have extended the various types of classical graph colouring methods to fuzzy graph colouring methods. In this study, we describe three basic types of fuzzy graph colouring methods namely, fuzzy vertex colouring, fuzzy edge colouring and fuzzy total colouring. We introduce a method to colour the vertices of the fuzzy graph using the polynomial ideal theory and find the fuzzy vertex chromatic number of the fuzzy graph. A practical example of scheduling committees meeting is given to demonstrate our proposed algorithm.

Keywords: fuzzy set; fuzzy graphs; classical graph; vertex colouring; edge colouring; total colouring; fuzzy vertex colouring; fuzzy edge colouring; fuzzy total colouring; fuzzy vertex chromatic number; fuzzy edge chromatic number; fuzzy total chromatic number; polynomial ideal; groebner basis.

DOI: 10.1504/IJAIP.2022.125238

International Journal of Advanced Intelligence Paradigms, 2022 Vol.23 No.1/2, pp.146 - 154

Received: 03 Jul 2017
Accepted: 23 Aug 2017
Published online: 05 Sep 2022 *

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