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Journal of Neutrosophic and Fuzzy Systems

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Online: 2771-6449 Print: 2771-6430
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Continuous publication

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Open access journal. All articles are freely available online with no APC.

Journal of Neutrosophic and Fuzzy Systems
Full Length Article

Volume 2Issue 2PP: 57-61 • 2022

Equitable Domination in Neutrosophic Graphs

M.M ullai 1* ,
S. Broumi 2 ,
Florentin Smarandache 3 ,
P.K.Santhi 4
1Department of Mathematics(DDE), Alagappa University, Karaikudi-630003.
2Laboratory of Information processing, University Hassan II, B.P 7955, Sidi Othman, Casablanca, Morocco.
3Department of Mathematics, University of New Mexico, 705 Gurley Avenue, Gallup, NM 87301, USA.
4Department of Mathematics, Jayaraj Annapackiam College for Women (Autonomous), Periyakulam, Theni(Dist)Tamilnadu, India
* Corresponding Author.
Received: January 20, 2022 Accepted: April 02, 2022

Abstract

This paper shows the equitable domination in neutrosophic graphs. In this proposed work, equitable neigh-bourhood of a vertex and equitabe degree are defined. Minimal neutrosophic dominating sets, minimal and maximal equitable independent sets,strong and weak equitable dominating sets in neutrosophic graphs are likewise settled. A few hypotheses on equitable domination in neutrosophic graphs are inferred with numeri-cal examples.

Keywords

Neutrosophic set neutrosophic graph neutrosophic equitable dominating set neutrosophic equi-table degree neutrosophic equitable independent set.

References

[1] Arumugam.S and S.Velammal, (1998). Edge domination in graphs, Taiwanese Journal of Mathematics , 2(2) , 173 - 179.

[2] Atanassov.K, (1965) . Intuitionistic fuzzy sets: theory and applications. Physica, New York, 1999.

[3] Ayyasamy.S and C.Natarajan, (2010). Strong (weak)domination in Fuzzy graphs. International Journal of computational and Mathematical secince.

[4] Chang.G.J, (1998) .Algorithmic aspects of domination in graphs, in:D.Z.Du, P.M. Pardalos (Eds.), Hand-book of Combinatorial Optimization, Vol. 3, Kluwer, Boston, MA, 339-405.

[5] Dharmalingam K.M, M.Rani (2014) Equitable domination in fuzzy graphs Volume 94 No. 5 2014, 661-667

[6] Haynes T.W et. al Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.

[7] Jayalakshmi.P.J and C.V.R.Harinarayanan .Independent and Total strong (weak) domination in Fuzzy Graph. International Journal of computational Engineering Research / Vol.04/Issue, 1, (71 - 74).

[8] John Stephan.J, A. Muthaiyan, N.Vinoth Kumar (2016). Equitable Dominating in an Intunionistic Fuzzy Graphs Volume 12, Number 3 (2016), pp. 2335-2341.

[9] Karunambigai.M.G ,S.Sivasankar and K.Palanivel, (2015). Some properties of a regular intuitionistic fuzzy graph,International Journal of Mathematics and Computation,26(4), 53-61.

[10] Karunambigai M.G, S.Sivasankar and K. Palanivel, (2010). Different types of domination in Intuitionistic Fuzzy Graph.. Annals of Pure and Applied Mathematics. 14.1, 87-101.

[11] Mordeson.J. N.,Nair P.S., Fuzzy graphs and Fuzzy Hyper graphs, Physica-Verlag, Heidelberg,1998, sec-ond edition (2001).

[12] Mullai.M., ” Dominations in Neutrosophic Graphs”, Neutrosophic Graph Theory and Algorithms, IGI Global Publications,USA, ISSN:2327-1981, pages 131-147(Nov 2019).

[13] Smarandache.F, (2015).Symbolic Neutrosophic Theory , Europanovaasbl, Brussels, 195p,.

[14] Smarandache.F, (2015). Refined Literal Indeterminacy and the multiplication Law of SubIndetermina-cies, Neutrosophic Sets and Systems, Vol. 9, 58.

[15] Somasundaram.A and S.Somasundaram,(1998).Domination in fuzzy graphs-I, Pattern Recognition Let-ters, 19(9), 787-791.

[16] Velammal.S and S.kathiresan(2012).Domination in Intuitionistic fuzzy graphs.2278-7844.

[17] Vekatasubramanian Swaminathan and Kuppusamy Markandan Dharmalingam. Degree Equitable Dom-ination on Graphs, Kragujevac Journal of Mathematics, Volume 35,Number 1,PP 177-183, (2011).

[18] Zadeh.L (1965),Fuzzy setzs, Inform and control,8,338-353.

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ullai, M.M, Broumi, S., Smarandache, Florentin, , P.K.Santhi. "Equitable Domination in Neutrosophic Graphs." Journal of Neutrosophic and Fuzzy Systems, vol. Volume 2, no. Issue 2, 2022, pp. 57-61. DOI: https://doi.org/10.54216/JNFS.020205
ullai, M., Broumi, S., Smarandache, F., , P. (2022). Equitable Domination in Neutrosophic Graphs. Journal of Neutrosophic and Fuzzy Systems, Volume 2(Issue 2), 57-61. DOI: https://doi.org/10.54216/JNFS.020205
ullai, M.M, Broumi, S., Smarandache, Florentin, , P.K.Santhi. "Equitable Domination in Neutrosophic Graphs." Journal of Neutrosophic and Fuzzy Systems Volume 2, no. Issue 2 (2022): 57-61. DOI: https://doi.org/10.54216/JNFS.020205
ullai, M., Broumi, S., Smarandache, F., , P. (2022) 'Equitable Domination in Neutrosophic Graphs', Journal of Neutrosophic and Fuzzy Systems, Volume 2(Issue 2), pp. 57-61. DOI: https://doi.org/10.54216/JNFS.020205
ullai M, Broumi S, Smarandache F, P. Equitable Domination in Neutrosophic Graphs. Journal of Neutrosophic and Fuzzy Systems. 2022;Volume 2(Issue 2):57-61. DOI: https://doi.org/10.54216/JNFS.020205
M. ullai, S. Broumi, F. Smarandache, P. , "Equitable Domination in Neutrosophic Graphs," Journal of Neutrosophic and Fuzzy Systems, vol. Volume 2, no. Issue 2, pp. 57-61, 2022. DOI: https://doi.org/10.54216/JNFS.020205
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