Some properties on fuzzy chromatic number of union of fuzzy graphs through α-cut graphs coloring

Abstract

We consider a fuzzy graph with a crisp vertex set V and a fuzzy edge set. A fuzzy graph has some α-cut graphs for α ∈ [0, 1] which are crisp graphs. Coloring of a fuzzy graph could be transformed into classical coloring of the α-cut graphs. Let and be two fuzzy graphs with fuzzy chromatic numbers and , respectively. Let be a union of and . By coloring of the α-cut graphs, we get the result that membership function of fuzzy chromatic number of the union satisfies a property for k ∈ {1, 2, 3, …, |V1 ⋃ V2|}. Furthermore, we also verify the connection between the fuzzy chromatic number and through a defuzzification dependent at a decision level.