Fuzzy Chromatic Polynomial of Fuzzy Graphs with Crisp and Fuzzy Vertices Using α-Cuts

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 on α-cuts of fuzzy graph. Two...

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Bibliographic Details
Published in:Advances in fuzzy systems 2019-01, Vol.2019 (2019), p.1-11
Main Authors: Abebe Ashebo, Mamo, Repalle, V. N. Srinivasa Rao
Format: Article
Language:English
Subjects:
Apexes
Coloring
Combinatorial analysis
Fuzzy sets
Graphs
Optimization
Polynomials
Register allocation
Traffic signals
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Summary: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 on α-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.
ISSN:1687-7101
1687-711X
DOI:10.1155/2019/5213020