Strong Vertex Coloring in Bipolar Fuzzy Graphs
DOI:
https://doi.org/10.26713/cma.v13i2.1810Keywords:
Bipolar fuzzy graphs, Bipolar Fuzzy Sets (BFS), Coloring, Strong edges and strong chromatic numberAbstract
Bipolar fuzzy graph (BFG) coloring techniques are used to solve many complex real world problems. The chromatic number of complement of BFG is obtained and compared with the chromatic number of the corresponding BFGs. This paper is an attempt to define coloring in a BFG based on strong edges. The strong chromatic number of complete BFG and BF tree are obtained.
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References
M. Akram, Bipolar fuzzy graphs, Information Sciences 181(24) (2011), 5548 – 5564, DOI: 10.1016/j.ins.2011.07.037.
M. Akram and N. Waseem, Novel applications of bipolar fuzzy graphs to decision making problems, Journal of Applied Mathematics and Computing 56 (2018), 73 – 91, DOI: 10.1007/s12190-016-1062-3.
M. Akram and W.A. Dudek, Regular bipolar fuzzy graphs, Neural Computing and Applications 21 (2012), 197 – 205, DOI: 10.1007/s00521-011-0772-6.
S. Mathew and M.S. Sunitha, Cycle connectivity in fuzzy graphs, Journal of Intelligent & Fuzzy System 24(3) (2013), 549 – 554, DOI: 10.3233/IFS-2012-0573.
S.Y. Mohamed and N. Subashini, Structures of edge regular bipolar fuzzy graphs, International Journal of Mathematics Trends and Technology 58(3) (2018), 215 – 220, DOI: 10.14445/22315373/IJMTT-V58P530.
S.Y. Mohamed and N. Subashini, Strength of strong cycle connectivity in BFG, Malaya Journal of Matematik 8(1) (2020), 62 – 66, DOI: 10.26637/MJM0801/0012.
B.A. Mohideen, Types of degrees in bipolar fuzzy graphs, Applied Mathematical Sciences 7(8) (2013), 4857 – 4866, DOI: 10.12988/ams.2013.37389.
S. Muñoz, M.T. Ortuño, J. Ramírez and J. Yáñeza, Coloring fuzzy graphs, Omega 33 (2005), 211 – 221, DOI: 10.1016/j.omega.2004.04.006.
B. Poornima and V. Ramaswamy, Application of edge coloring of a fuzzy graph, International Journal of Computer Applications 6(2) (2010), 14 – 19, https://www.ijcaonline.org/volume6/number2/pxc3871371.pdf.
S. Samanta, T. Pramanik and M. Pal, Fuzzy coloring of fuzzy graphs, Afrika Matematika 27 (2016), 37 – 50, DOI: 10.1007/s13370-015-0317-8.
M. Tom and M.S. Sunitha, Sum distance in fuzzy graphs, Annals of Pure and Applied Mathematics 7(2) (2014), 73 – 89, http://www.researchmathsci.org/apamart/apam-v7n2-9.pdf.
L.A. Zadeh, Fuzzy sets, Information and Control 8(3) (1965), 338 – 353, DOI: 10.1016/S0019-9958(65)90241-X.
W.R. Zhang, Bipolar fuzzy sets and relations: A computational framework for cognitive modeling and multiagent decision analysis,in: NAFIPS/IFIS/NASA ’94. Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference. The Industrial Fuzzy Control and Intellige, 1994, pp. 305 – 309, DOI: 10.1109/IJCF.1994.375115.




