Fuzzy Graph Coloring Using Gröbner Basis

Abstract

Fuzzy graph theory has an important role in modeling uncertainty in the real environment. In this work, a new approach is proposed concerning the graph coloring problem of a fuzzy graph using Gröbner basis, and a generalization of the classical crisp chromatic number of a graph. This approach is established on the successive coloring functions of the crisp graphs. Using this method, we can determine whether or not, for a fixed [Formula: see text], the given graph can be colored. If such a coloring exists, the number of distinct [Formula: see text]-colorings and chromatic number in the given fuzzy graph can be obtained. As an application, we analyze the traffic lights problem by using this method.