A new approach for determining fuzzy chromatic number of fuzzy graph

Abstract

Abstract

A fuzzy graph referred in this paper is a graph with crisp vertex set and fuzzy edge set. The most important issue in the coloring problem of fuzzy graph is to construct a method for finding the chromatic number of fuzzy graph. Most of the methods that many researchers had been done still result crisp chromatic number. In this paper, we propose a new approach to determine fuzzy chromatic set of fuzzy graph. In our proposed method, the fuzzy chromatic set of fuzzy graph is constructed through its δ-chromatic number. Further, we investigate some properties of the fuzzy chromatic set of fuzzy graph. We show that fuzzy chromatic set of fuzzy graph is a discrete fuzzy number and then it is called by fuzzy chromatic number. To the best of our knowledge, no one has determined fuzzy chromatic number of fuzzy graph through its δ-chromatic number before now. Finally, a fuzzy chromatic algorithm based on the new approach is proposed.