Fuzzy colouring of m-polar fuzzy graph and its application

Article type: Research Article

Authors: Mahapatra, Tanmoy | Pal, Madhumangal^{; *}

Affiliations: Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, India

Correspondence: [*] Corresponding author. Madhumangal Pal, Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, India. E-mail: mmpalvu@mail.vidyasagar.ac.in.

Abstract: In this article, a new idea of fuzzy coloring of m-polar fuzzy graph is presented while establishing the relationship between chromatic number of m-polar fuzzy graph and it’s underlying crisp graph. Some properties of m-polar fuzzy graph and new concepts of independently strong edge and independently weak edge in m-polar fuzzy graph are proved. The differences between fuzzy coloring of fuzzy graph and m-polar fuzzy graph are discussed. It is also shown that a m-polar fuzzy graph can be decomposed into m fuzzy graphs. Again, from m isomorphic fuzzy graph one can construct a m-polar fuzzy graph. A relation among chromatic numbers of m-polar fuzzy graph and m such graphs is established. Lastly a real life application of the fuzzy coloring is discussed.

Keywords: m-polar fuzzy graph, α-strength cut graphs, independently weak edges, independently strong edges, chromatic number

DOI: 10.3233/JIFS-181262

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 6, pp. 6379-6391, 2018