Number of possible captures in a chess puzzle move using the fuzzy colouring technique

Article type: Research Article

Authors: Kadeeja Mole, K.P.^{; *} | Sameena, Kalathodi

Affiliations: Department of Mathematics, MES Mampad College, Mampad, Kerala, India

Correspondence: [*] Corresponding author: K.P. Kadeeja Mole, Department of Mathematics, MES Mampad College, Mampad, Kerala, 676542, India. Tel.: +918921696968; E-mail: [email protected].

Abstract: In this work, several operations on fuzzy graphs are introduced: u-product, strong edge product, and k th power. The relationship between the fuzzy chromatic number of resultant fuzzy graphs of operations union, join, and newly developed operations and the fuzzy chromatic number of associated fuzzy graphs is also investigated using fuzzy colouring techniques. The number of captures in a chess puzzle move is calculated using the fuzzy colouring approach.

Keywords: Fuzzy graph, fuzzy chromatic number, operations of fuzzy graphs, strong edge, fuzzy colouring

DOI: 10.3233/JIFS-223263

Journal: Journal of Intelligent & Fuzzy Systems, vol. 45, no. 1, pp. 549-561, 2023