Effective Edge Domination in iterated Jump Graph of Intuitionistic Fuzzy Graph
DOI:
https://doi.org/10.12723/mjs.69.9Keywords:
Intuitionistic Fuzzy Jump graph, Effective edge dominating set, Evanesce numberAbstract
Intuitionistic Fuzzy Graphs (InFGs) serve as a sophisticated framework for modeling complex and uncertain phenomena across diverse domains, such as decision-making, economics, medicine, computer science, and engineering. In this research, we develop and analyse the properties of jump graphs in the context of InFGs. The vertex set of the jump graph J(G) of a graph G is defined as the edge set of G, with adjacency between vertices in J(G) established if and only if the corresponding edges in G are non-incident. We systematically construct sequences of jump graphs for InFGs through iterative processes and investigate the structural characteristics of these sequences. Moreover, we introduce the concept of an effective edge dominating set for jump graphs of InFGs and rigorously determine the effective edge domination number for certain classes of graphs. These contributions enhance the theoretical foundation of InFGs and extend
their applicability to solving real-world problems characterized by uncertainty and complexity
References
Atanassov, Krassimir T. ”New operations defined over the Intuitionistic Fuzzy sets.” Fuzzy sets and Systems 61.2 (1994): 137-142.
Atanassov, Krassimir. ”Review and new results on Intuitionistic Fuzzy sets.” preprint Im MFAIS-1-88, Sofia 5.1 (1988).
Rosenfeld, Azriel. ”Fuzzy graphs.” Fuzzy sets and their applications to cognitive and decision processes. Academic press, 1975. 77-95.
Akram, Muhammad, and R. Parvathi. ”Properties of Intuitionistic Fuzzy line graphs.” Notes on Intuitionistic Fuzzy sets 18.3 (2012): 52-60.
Gupta, Preeti. ”Domination in graph with application.” Indian J. Res 2.3 (2013): 115-117.
Arumugam, S., and S. Velammal. ”Edge domination in graphs.” Taiwanese journal of Mathematics (1998): 173-179.
Parvathi, R., and G. Thamizhendhi. ”Domination in Intuitionistic Fuzzy graphs.” Notes on Intuitionistic Fuzzy Sets 16.2 (2010): 39-49.
James, Josna, and Shiny Jose. ”Intuitionistic fuzzy graph of third type.” International journal of Scientific Research in Mathematical and Statistical Sciences 6.1 (2019): 221-224.
James, Josna, and Shiny Jose. ”Path Induced Vertex Covering for Intuitionistic Fuzzy Graph and its Application in Disaster Management.” Mapana Journal of Sciences 21.3 (2022).
Anupama, S. B., Y. B. Maralabhavi, and Venkanagouda M. Goudar. ”Connected domination number of a jump graph.” Journal of Computer and Mathematical Sciences 6.10(2015): 538-545.
Anupama, S. B., Y. B. Maralabhavi, and V. M. Goudar. ”Some Domination Parameters on Jump graph.” (2017): 47-55.
Parvathi, R., and M. G. Karunambigai. ”Intuitionistic Fuzzy graphs.” Computational intelligence, theory and applications. Springer, Berlin, Heidelberg, 2006. 139-150.
Karunambigai, M. G., R. Parvathi, and O. K. Kalaivani. ”A study on atanassov’s Intuitionistic Fuzzy graphs.” 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011). IEEE, 2011.
Rao, N. Pratap Babu. ”On Non Bondage Number of a Jump Graph.” International Journal of Mathematics Trends and Technology 57.4 (2018): 292-295.
Karunambigai, M. G., S. Sivasankar, and K. Palanivel. ”Some properties of a regular Intuitionistic Fuzzy graph.” International Journal of Mathematics and Computation 26.4
(2015): 53-61.
Senthilkumar, V. ”Types of domination in Intuitionistic Fuzzy graph by strong arc and effective ARC.” Bulletin of Pure & Applied Sciences-Mathematics and Statistics 37.2 (2018): 490-498.
Karunambigai, M. G., S. Sivasankar, and K. Palanivel. ”Different types of domination in Intuitionistic Fuzzy graph.” Annals of pure and Applied Mathematics 14.1 (2017): 87-101
Additional Files
Published
Issue
Section
License
Copyright (c) 2024 Josna James, Josna James
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.