Fuzzy Chromatic Polynomial of Fuzzy Graphs with Crisp and Fuzzy Vertices Using α-Cuts. (2nd May 2019)

• Record Type: Journal Article
• Authors: Abebe Ashebo, Mamo; Repalle, V. N. Srinivasa Rao
• Other Names: Dvorák Antonin Academic Editor.
• Is Part Of: Advances in fuzzy systems. Volume 2019(2019)
• Publication Date: 2019-05-02
• Subjects: Fuzzy systems -- Periodicals; Systèmes flous; Fuzzy systems; Periodicals; 511.313
• DOI: 10.1155/2019/5213020
• Languages: English
• ISSNs: 1687-7101

Abstract

Abstract : Coloring of fuzzy graphs has many real life applications in combinatorial optimization problems like traffic light system, exam scheduling, register allocation, etc. In this paper, the concept of fuzzy chromatic polynomial of fuzzy graph is introduced and defined based onα -cuts of fuzzy graph. Two different types of fuzziness to fuzzy graph are considered in the paper. The first type was fuzzy graph with crisp vertex set and fuzzy edge set and the second type was fuzzy graph with fuzzy vertex set and fuzzy edge set. Depending on this, the fuzzy chromatic polynomials for some fuzzy graphs are discussed. Some interesting remarks on fuzzy chromatic polynomial of fuzzy graphs have been derived. Further, some results related to the concept are proved. Lastly, fuzzy chromatic polynomials for complete fuzzy graphs and fuzzy cycles are studied and some results are obtained.