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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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2019/5213020 |
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| author | Mamo Abebe Ashebo V. N. Srinivasa Rao Repalle |
| author_facet | Mamo Abebe Ashebo V. N. Srinivasa Rao Repalle |
| author_sort | Mamo Abebe Ashebo |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2aa238ccc76c4bf0b6fcedb002384b24 |
| institution | Kabale University |
| issn | 1687-7101 1687-711X |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| spelling | doaj-art-2aa238ccc76c4bf0b6fcedb002384b242025-02-03T01:01:57ZengWileyAdvances in Fuzzy Systems1687-71011687-711X2019-01-01201910.1155/2019/52130205213020Fuzzy Chromatic Polynomial of Fuzzy Graphs with Crisp and Fuzzy Vertices Using α-CutsMamo Abebe Ashebo0V. N. Srinivasa Rao Repalle1Department of Mathematics, Wollega University, Nekemte, EthiopiaDepartment of Mathematics, Wollega University, Nekemte, EthiopiaColoring 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.http://dx.doi.org/10.1155/2019/5213020 |
| spellingShingle | Mamo Abebe Ashebo V. N. Srinivasa Rao Repalle Fuzzy Chromatic Polynomial of Fuzzy Graphs with Crisp and Fuzzy Vertices Using α-Cuts Advances in Fuzzy Systems |
| title | Fuzzy Chromatic Polynomial of Fuzzy Graphs with Crisp and Fuzzy Vertices Using α-Cuts |
| title_full | Fuzzy Chromatic Polynomial of Fuzzy Graphs with Crisp and Fuzzy Vertices Using α-Cuts |
| title_fullStr | Fuzzy Chromatic Polynomial of Fuzzy Graphs with Crisp and Fuzzy Vertices Using α-Cuts |
| title_full_unstemmed | Fuzzy Chromatic Polynomial of Fuzzy Graphs with Crisp and Fuzzy Vertices Using α-Cuts |
| title_short | Fuzzy Chromatic Polynomial of Fuzzy Graphs with Crisp and Fuzzy Vertices Using α-Cuts |
| title_sort | fuzzy chromatic polynomial of fuzzy graphs with crisp and fuzzy vertices using α cuts |
| url | http://dx.doi.org/10.1155/2019/5213020 |
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