[J,K]-SET DOMINATION IN FUZZY GRAPHS
Main Article Content
Abstract
Domination is a theoretical concept in graph theory. In this paper, [j, k]- set domination in Fuzzy Graphs is introduced. We study
some important properties and derive some results. By [J, K]-set domination, a subset D in a Fuzzy graph G = (V, E) is a [j,k]-
set, if every Fuzzy vertex v that is not in the dominating set is adjacent to at least j but not more than k vertices in D. We
consider the vertices j and k as small positive integers. The Domination number is denoted by γ[j,k](
G), which is the minimum
cardinality of a dominating set.
Downloads
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
You are free to:
- Share — copy and redistribute the material in any medium or format for any purpose, even commercially.
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
- Attribution — You must give appropriate credit , provide a link to the license, and indicate if changes were made . You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
Notices:
You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation .
No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.
References
[1] Anu Shree Bhattacharya. Madhumangal Pal, Fuzzy covering problem of fuzzy graphs and its application to investigate the Indian economy in the new normal, Journal of Applied Mathematics and Computing.
[2] Enrico Enriquez, Grace Estrada, Carmelitaloquias, Reuellaj Bacalso and Lannden Ocambo Domination in Fuzzy directed Graphs.
[3] S.Ismail Mohideen and A Mohamed Ismayil, Domination in Fuzzy Graphs. A New Approach International Journal of Computational Science and Mathematics, ISSN 0974-3189, Volume 2, Number 3(2010) PD101-107.
[4] D. Jayanthi Prasanna, Domination in Fuzzy Graphs, International Journal of Advanced Research in Engineering and Technology, Vol. 10, Issue 6, Nov-Dec 2019 pp-442-447
[5] Haynes T.W, Hedetniemi S.T, and Slater P.J, Fundamentals of domination in graphs. New York Dekker, 1998. [6] O.T.Manjula, M.S.Sunitha, Strong domination in Fuzzy Graphs, Fuzzy Inf. Eng.(2015): 369-377
[7] A. Muneera, Dr R.V.N. Srinivas Rao, Study on Fuzzy Graphs and Applications. Bulletin of Mathematics and Statistics Research, vol. 4, SL 2016; ISSN:2348-0580
[8] N. Murugesan and Deepa.S.Nair,(1,2)-Domination in graphs, J. Maths. Comput. Science 2 (2012) No 4, 774- 783 ISSN: 1927-5307.
[9] Mustapha chellalia, Teresa w. Haynes, Stephen T.H. Hedetniemia, al [1, 2]-sets in graphs, Discrete Applied Mathematics 161 (2013) 2885-2893.
[10] A. Nagoor Gani and K.Prasanna Devi 2-Domination in Fuzz graphs International Journal
[11] Fuzzy mathematical archive vol.9, no 1, 2015, 119-124 A. Nagoor Gani, V T. Chandrasekaran Domination in Fuzzy graphs Adv. in Fuzzy sets and systems I(1)(2006) 17-26
[12] A. Nagoor Gani, P. Muruganantham and A. Nafiunisha, A new type of dominating Fuzzy Graphs, Advances and Applications in mathematical sciences vol 20, Issue 6, April 2021, pages 1085-1091.
[13] S.Ramya and S.Lavanya, perfect vertex (Edge) Domination in Fuzzy graphs, Indian Journal of Science and Technology, Volume 9(4), Jan 2016
[14] Rosenfield. A Fuzzy Graphs in Fuzzy sets and their applications Zadeh. L. A. et al. Academic Press New York, NY, USA, 1975, pp. 77-95
[15] N. Sarala, T. Kavitha, (1, 2)-Vertex domination in Fuzzy line Graphs, International Journal of Engineering and Science and Mathematics Vol 5, Issue 4, Dec 2016.
[16] Somasundaram A, Somasundaram S. Domination in Fuzzy Graphs–I Pattern Recognition 1998, Vol 19,787- 791
[17] D.B. West, Introduction to Graph Theory, Prentice Hall, 1996.
[18] Zadeh L.A. Fuzzy sets inf. control 1965, 8, 338-353 [13] Sustarevas, J. et al. MAP-a mobile agile printer robot for on-site construction. In Proc. 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2441–2448 (IEEE, 2018).
[19] R. K. Kaushik, Anjali and D. Sharma, "Analysing the Effect of Partial Shading on Performance of Grid Connected Solar PV System", 2018 3rd International Conference and Workshops on Recent Advances and Innovations in Engineering (ICRAIE), pp. 1-4, 2018.