A new approach for determining fuzzy chromatic number of fuzzy graph

作者：Rosyida Isnaini^*; Widodo; Indrati Ch Rini; Sugeng Kiki A

来源：Journal of Intelligent and Fuzzy Systems, 2015, 28(5): 2331-2341.

DOI：10.3233/IFS-141521

• Fuzzy graph coloring
• delta-chromatic number
• fuzzy chromatic set
• discrete fuzzy number
• fuzzy chromatic number

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 delta-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 delta-chromatic number before now. Finally, a fuzzy chromatic algorithm based on the new approach is proposed.

• 出版日期2015