Method for Finding the Chromatic Number of Intuitionistic Fuzzy Graph

Abstract

In this paper a method for determining the chromatic number and the problem of fuzzy graph coloring is discussed. The problem of attributing colors to predetermined elements of a graph with respect to certain restrictions and constraints under uncertainty in considered. The process of vertex coloring in crisp graph presupposes that no two adjacent vertices have the same color, so the concept of chromatic number in graph defines the minimum number of colors that we may need to color the graph. The concept of a chromatic number search of fuzzy graph is extended to intuitionistic case in this paper. The chromatic number as an intuitionistic fuzzy set determines the greatest degree of separability of the vertices of the graph when it is colored with a given number of colors. A method for determining the chromatic number is proposed and the algorithm for determining a chromatic number is considered as well.