On regular spherical fuzzy graph

Document Type : Research Paper

Authors

1 PG and Research Department of Mathematics, Rajah Serfoji Government College (Autonomous), Affiliated to Bharathidasan University, Thanjavur, India-613005.

2 Research Scholar,_x000D_ Department of Mathematics,_x000D_ Rajah Serfoji Government College(Autonomous),_x000D_ (Affiliated to Bharathidasan University),_x000D_ Thanjavur-613005

Abstract

A spherical fuzzy set is an advanced extension of clas-sical fuzzy set in which it has an added advantage to deal with a
wider sense of applicability in uncertain situations. In this paper,regular spherical fuzzy graphs and totally regular spherical fuzzy graphs are introduced. A necessary and sufficient condition for reg-ular spherical fuzzy graphs is given.
Some properties of regular and totally regular spherical fuzzy graphs are studied.

Keywords


[1] M. Akram, D. Saleem and T. Al-Hawary, Spherical fuzzy graphs with application to decision-making, Mathematical and Computational Applications, 25, 8(2020),1-32.
[2] A. Guleria and R.K. Bajaj, T-Spherical fuzzy graphs: operations and applications in various selection processes, Arabian Journal for Science and Engineering, 45 (2020), 2177–2193.
[3] I. Gutman, A. Betten, A.Kohner, R. Laue and A. Wassermann, eds., The en-ergy of a graph: old and new results, Algebraic Combinatorics and Applications,Springer, Berlin, (2001), 196-211.
[4] A. N. Gani and K. Radha, On regular fuzzy graphs, Journal of Physical Sciences,12(2010), 33–40.
[5] U. Kifayat, Q. Khan and N. Jan, Similarity measures for T-spherical fuzzy sets with applications in pattern recognition, Symmetry, 10(6)(2018), 1–14.
[6] T. Mahmood, U. Kifayat, Q. Khan and N.Jan, An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy set,Neural Computing and Applications, 31(2019), 7041-7053.
[7] S.Y. Mohamed and A. M. Ali, Degree of a vertex in complement of modular product of intuitionistic fuzzy graphs, Journal of Physical Sciences, 24(2019),115–124.
[8] S. Y. Mohamed and A. M. Ali, Modular product on intuitionistic fuzzy graphs,International Journal of Innovative Research in Science, Engineering and Tech-nology, 6(9)(2017), 19258–19263.
[9] S. Y. Mohamed and A. M. Ali, Max-product on intuitionistic fuzzy graph, Proceeding of 1st International Conference on Collaborative Research in Mathematical Sciences, 1(2017), 181–185.
[10] S. Y. Mohamed and A. M. Ali, Energy of Spherical Fuzzy Graphs, Advances in Mathematics: Scientific Journal, 9(1)(2020), 321–332.
[11] S. Saxena, A. Thapar and R. Bansal, Total Fuzzy Coloring, Journal of Hyperstructures, 11(1)(2022), 84–108.
[12] C. Zuo, A. Pal and A. Dey, New Concepts of Picture Fuzzy Graphs with Application, Mathematics, 7(470)(2019), 1 - 18.