Strength of strong cycle connectivity in bipolar fuzzy graphs

S. Yahya Mohamed; N. Subashini

doi:10.26637/MJM0801/0012

Abstract

In this paper, the notion of cycle connectivity of bipolar fuzzy graphs is introduced. The concept of strong edge, $P$ cut node, $P$-bridge and $\theta$ - evaluation of bipolar fuzzy graphs are studied. The cycle connectivity of bipolar fuzzy trees, bipolar fuzzy cycles and complete bipolar fuzzy graphs are obtained. A condition for complete bipolar fuzzy graphs to have cyclic cut-nodes is obtained.

Keywords:

Bipolar Fuzzy Graph (BFG), Bipolar Fuzzy Strength (BFS), Bipolar Fuzzy Tree (BFT), θ -evaluation, α -Strong, β-Strong, δ-arc

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

S. Yahya Mohamed PG and Research Department of Mathematics, Government Arts College, Affiliated to Bharathidasan University, Tiruchirappalli-620022, Tamil Nadu, India.
N. Subashini Research Scholar (Part-Time), Government Arts College, Affiliated to Bharathidasan University, Tiruchirappalli-620022, Tamil Nadu, India.

Pages: 62-66
Date Published: 01-01-2020
Vol. 8 No. 01 (2020): Malaya Journal of Matematik (MJM)

M. B. Ahamed, Types of degrees in bipolar fuzzy graphs, Appl. Math. Sci. (Ruse), 7(2013), 4857-4866.

M.Akram, Bipolar fuzzy graphs, Information Sciences, 2011, 12-23.

M. Akram, W. A. Dudek, Regular bipolar fuzzy graphs, Neural Comput. Appl., 21(2012), 197-205.

M. Akram, N. Waseem, Novel applications of bipolar fuzzy graphs to decision making problems, J. Appl. Math. Comput., 56(2018), 73-91.

S. Mathew and M.S. Sunitha, Cycle connectivity in fuzzy graphs, Journal of Intelligent and Fuzzy System, 24(2013), $549-554$.

S. Yahya Mohamed, A. Mohamed Ali, Interval-Valued Pythagorean Fuzzy Graph, Journal of Computer and Mathematical Sciences, 9(10)(2018), 1497-1511.

S.Yahya Mohamed, A. Mohamed Ali, Modular product on intuitionistic fuzzy graphs, International Journal of Innovative Research in Science, Engineering and Technology, 6(9)(2017), 19258-19263.

S. Yahya Mohamed and N. Subashini, Connectivity in a Bipolar Fuzzy Graph and its Complement, Annals of Pure and Applied Mathematic, 15(1)(2017), 89-95.

S.Yahya Mohamed and N. Subashini, Structures of edge regular bipolar fuzzy graphs, International Journal of Mathematics Trends and Technology, 58(3)(2018), 215220.

S. Yahya Mohamed and N. Subashini, Bipolar Fuzzy Graphs Based on Eccentricity Nodes, Journal of Applied Science and Computations, 5(11)(2018), 153-158.

S. Yahya Mohamed and N. Subashini, Some types of paths in a Bipolar Fuzzy Graphs, Journal of Applied Science and Computations, 6(6)(2019), 305-308.

L.A.Zadeh, Fuzzy sets, Information and control, 8(1965), $338-353$.

W. R. Zhang, Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multi-agent decision analysis, Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference, 1994 (1994), 305-309.