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Applications of Edge Colouring of Fuzzy Graphs
Volume 31, Issue 2 (2020), pp. 313–330
Pub. online: 2 April 2020      Type: Research Article      Open accessOpen Access
Received
1 October 2018
Accepted
1 February 2020
Published
2 April 2020

Abstract

Colouring of graphs is being used in several representations of real world systems like map colouring, traffic signalling, etc. This study introduces the edge colouring of fuzzy graphs. The chromatic index and the strong chromatic index are defined and related properties are investigated. In addition, job oriented web sites, traffic light problems have been presented and solved using the edge colouring of fuzzy graphs more effectively.

References

 
Bershtein, L.S., Bozhenuk, A.V. (2001). Fuzzy coloring for fuzzy graphs. In: lEEE International Fuzzy Systems Conference, pp. 1101–1103.
 
Chen, L., Peng, J., Zhang, B., Li, S. (2017). Uncertain programming model for uncertain minimum weight vertex covering problem. Journal of Intelligent Manufacturing, 28(3), 625–632.
 
Kauffman, A. (1973). Introduction a la Theorie des Sous-emsembles Flous. Masson et Cie Editeurs, Paris.
 
Kishore, A., Sunitha, M.S. (2014). Strong chromatic number of fuzzy graphs. Annals of Pure and Applied Mathematics, 7, 52–60.
 
Kishore, A., Sunitha, M.S. (2016). On Injective Coloring of Graphs and Chromaticity of Fuzzy Graphs. LAP Lambert Academic Publishing.
 
Mahapatra, R., Samanta, S., Pal, M., Qin, X. (2019a). RSM index: a new way of link prediction in social networks. Journal of Intelligent and Fuzzy Systems, 37, 2137–2151. https://doi.org/10.3233/JIFS-181452.
 
Mahapatra, R., Samanta, S., Allahviranloo, T., Pal, M. (2019b). Radio fuzzy graphs and assignment of frequency in radio stations. Computational and Applied Mathematics. https://doi.org/10.1007/s40314-019-0888-3.
 
Mordeson, J.N., Nair, P.S. (2000). Fuzzy Graphs and Hypergraphs. Physica Verlag.
 
Munoz, S., Ortuno M, T., Ramirez, J., Yanez, J. (2005). Coloring fuzzy graphs. Omega, 33(3), 211–221.
 
Rosenfeld, A. (1975). Fuzzy graphs. In: Zadeh, L.A., Fu, K.S., Shimura, M. (Eds.), Fuzzy Sets and Their Applications. Academic Press, New York, pp. 77–95.
 
Rosyida, I., Widodo, Indrati, C.R., Ariyanti, K., (2015). A new approach in determining fuzzy chromatic index of a fuzzy graph. Journal of Intelligent and Fuzzy Systems, 28(5), 2331–2341.
 
Rosyida, I., Peng, J., Chen, L., Widodo, I.C.R., Sugeng, K.A. (2016). An uncertain chromatic index of an uncertain graph based on alpha-cut coloring. Fuzzy Optimization and Decision Making. https://doi.org/10.1007/s10700-016-9260-x.
 
Samanta, S., Pal, M. (2013). Fuzzy k-competition graphs and p-competition fuzzy graphs. Fuzzy Engineering and Information, 5(2), 191–204.
 
Samanta, S., Pal, M. (2015). Fuzzy planar graphs. IEEE Transaction on Fuzzy Systems, 23(6), 1936–1942.
 
Samanta, S., Sarkar, B., Shin, D., Pal, M. (2016a). Completeness and regularity of generalized fuzzy graphs. Springer Plus. https://doi.org/10.1186/s40064-016-3558-6.
 
Samanta, S., Pramanik, T., Pal, M. (2016b). Colouring of fuzzy graphs. Afrika Matematica, 27, 37–50.
 
Sarkar, B., Samanta, S. (2017). Generalized fuzzy trees. International Journal of Computational Intelligence Systems, 10, 711–720.

Biographies

Mahapatra Rupkumar
rupkumarmath@gmail.com

R. Mahapatra is currently a research scholar, at the Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, India. His research interest includes fuzzy graph theory.

Samanta Sovan
ssamantavu@gmail.com

S. Samanta is an assistant professor at the Department of Mathematics, Tamralipta Mahavidyalaya (Vidyasagar University). He is engaged in the research of fuzzy systems, graph theory, social network analysis, etc. He published more than 50 research articles in different reputed SCI/SCIE, scopus journals. Also, he published two edited books on mathematics and authored one textbook on graph theory. He is currently an associate editor of Journal of Applied Mathematics and Computing.

Pal Madhumangal
mmpalvu@gmail.com

M. Pal is currently a professor of applied mathematics at Vidyasagar University. He has received gold and silver medals from Vidyasagar University for the first and second ranks in MSc and BSc examinations, respectively. Also, he received a computer division medal from Institute of Engineers (India) in 1996 for the best research work. In 2013, he received Bharat Jyoti Award for the significant contribution in academics. Prof. Pal has successfully guided 34 research scholars for PhD degrees and has published more than 320 articles in international and national journals. His specializations include algorithmic and fuzzy graph theory, fuzzy matrices, genetic algorithms and parallel algorithms. Prof. Pal is the author of eight textbooks published in India and United Kingdom and two edited books. He has published 17 chapters in several edited books. Prof. Pal completed three research projects funded by UGC and DST, and one project is still in progress. Prof. Pal is the editor-in-chief of Journal of Physical Sciences, Annals of Pure and Applied Mathematics, area editor of International Journal of Computational Intelligence Systems (SCI Indexed Journal) and a member of the editorial boards of many journals. He is also a member of the American Mathematical Society, USA, Calcutta Mathematical Society, Advanced Discrete Mathematics and Application, Neutrosophic Science International Association, USA, etc. He is a member of several administrative and academic bodies in Vidyasagar University and other institutes.


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Keywords
edge colouring chromatic index fuzzy graphs

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