A new approach for determining fuzzy chromatic number of fuzzy graph

Isnaini Rosyida, Widodo, Ch Rini Indrati, Kiki Ariyanti

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

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

Original languageEnglish
Pages (from-to)2331-2341
Number of pages11
JournalJournal of Intelligent and Fuzzy Systems
Volume28
Issue number5
DOIs
Publication statusPublished - 23 Jun 2015

Keywords

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

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