Bridge domination in fuzzy graphs

Shanmugam, Sivasankar; Aishwarya, Thirumal Perumal; Shreya, Nagesh

doi:10.22105/jfea.2023.382170.1251

Document Type : Research Paper

Authors

¹ Department of Mathematics, R V Institute of Technology and Management, Bangalore-560076.

² Department of Electronics and Communication Engineering, R V institute of Technology and Management, Bangalore-560076.

https://doi.org/10.22105/jfea.2023.382170.1251

Abstract

In communication networks, strong connectivity between nodes is critical. The failure of strong connectivity between nodes may jeopardize the network’s stability. In fuzzy graphs, various dominating sets using strong edges are identified to avoid network stability. In this paper, the concept of bridge domination set and bridge domination number in fuzzy graphs is introduced. A few prominent properties of bridge domination numbers are chosen and analyzed using relevant examples. The bridge domination number of fuzzy trees, constant fuzzy cycles, and complete fuzzy and bipartite fuzzy graphs are identified. The use of bridge domination in a partial mesh topology to ensure network continuity is demonstrated in the event of a node failure.

Keywords

Main Subjects

Fuzzy sets and their variants

References

[1] Ore, O. (1962). Theory of graphs. American Mathematical Society.

[2] Berge, C. (1973). Graphs and hypergraphs. North-Holland Publishing Company.

[3] Sampathkumar, E., & Walikar, H. B. (1979). The connected domination number of a graph. Journal of mathematical physical sciences, 13(6), 607–613.

[4] Banerjee, A. (2021). On the spectrum of hypergraphs. Linear algebra and its applications, 614, 82–110.

[5] Rosenfeld, A. (1975). Fuzzy graphs. In Fuzzy sets and their applications to cognitive and decision processes (pp. 77–95). Elsevier.

[6] Somasundaram, A., & Somasundaram, S. (1998). Domination in fuzzy graphs-I. Pattern recognition letters, 19(9), 787–791.

[7] Nagoorgani, A., & Chandrasekaran, V. T. (2006). Relations between the parameters of independent domination and irredundance in fuzzy graph. Fuzzy sets and systems, 1(1), 17–26.

[8] Binu, M., Mathew, S., & Mordeson, J. N. (2021). Connectivity status of fuzzy graphs. Information sciences, 573, 382–395.

[9] Binu, M., Mathew, S., & Mordeson, J. N. (2020). Cyclic connectivity index of fuzzy graphs. IEEE transactions on fuzzy systems, 29(6), 1340–1349.

[10] Nazeer, I., Rashid, T., & Garcia Guirao, J. L. (2021). Domination of fuzzy incidence graphs with the algorithm and application for the selection of a medical lab. Mathematical problems in engineering, 2021, 1–11. DOI:10.1155/2021/6682502

[11] Chen, X. G., Sohn, M. Y., & Ma, D. X. (2019). Total efficient domination in fuzzy graphs. IEEE access, 7, 155405–155411. DOI:10.1109/ACCESS.2019.2948849

[12] Karunambigai, M. G., Sivasankar, S., & Palanivel, K. (2017). Secure domination in fuzzy graphs and intuitionistic fuzzy graphs. Annals of fuzzy mathematics and informatics, 14(4), 419–443.

[13] Karunambigai, M. G., Sivasankar, S., & Palanivel, K. (2018). Secure edge domination and vertex edge domination in intuitionistic fuzzy graphs. International journal of mathematical archive, 9(1), 190-196.

[14] Mathew, S., & Sunitha, M. S. (2013). Strongest strong cycles and θ-fuzzy graphs. IEEE transactions on fuzzy systems, 21(6), 1096–1104. DOI:10.1109/TFUZZ.2013.2243154

[15] Manjusha, O. T. (2023). Global domination in Fuzzy graphs using Strong arcs. Journal of fuzzy extension and applications, 4(1), 8–17.

[16] Manjusha, O. T., & Sunitha, M. S. (2015). Strong domination in fuzzy graphs. Fuzzy information and engineering, 7(3), 369–377.

[17] Das, S. K. (2021). Optimization of fuzzy linear fractional programming problem with fuzzy numbers. Big data and computing visions, 1(1), 30–35.

[18] El-Shorbagy, M. A., Mousa, A. A. A., ALoraby, H., & Abo-Kila, T. (2020). Evolutionary algorithm for multi-objective multi-index transportation problem under fuzziness. Journal of applied research on industrial engineering, 7(1), 36–56.

[19] El-Morsy, S. A. (2022). Optimization of fuzzy zero-base budgeting. Computational algorithms and numerical dimensions, 1(4), 147–154.

[20] Rashmanlou, H., Muhiuddin, G., Amanathulla, S. K., Mofidnakhaei, F., & Pal, M. (2021). A study on cubic graphs with novel application. Journal of intelligent and fuzzy systems, 40(1), 89–101.

[21] Rashmanlou, H., Borzooei, R. A., Shoaib, M., Talebi, Y., Taheri, M., & Mofidnakhaei, F. (2020). New way for finding shortest path problem in a network. Journal of multiple-valued logic and soft computing, 34(5–6), 451–460.

[22] Shao, Z., Kosari, S., Shoaib, M., & Rashmanlou, H. (2020). Certain concepts of vague graphs with applications to medical diagnosis. Frontiers in physics, 8, 357. DOI:10.3389/fphy.2020.00357

[23] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353.

[24] Zeng, S., Shoaib, M., Ali, S., Smarandache, F., Rashmanlou, H., & Mofidnakhaei, F. (2021). Certain properties of single-valued neutrosophic graph with application in food and agriculture organization. International journal of computational intelligence systems, 14(1), 1516–1540.

[25] Mordeson, J. N., & Nair, P. S. (2001). Fuzzy graphs and fuzzy hypergraphs. Physica Verlag, Heidelberg.

Journal of Fuzzy Extension and Applications

Bridge domination in fuzzy graphs

References

References

Volume 4, Issue 3
July 2023
Pages 148-154

Bridge domination in fuzzy graphs

References

References

Volume 4, Issue 3July 2023Pages 148-154

Volume 4, Issue 3
July 2023
Pages 148-154