Volume 2 , Issue 2 , PP: 57-61, 2022 | Cite this article as | XML | Html | PDF | Full Length Article
M.M ullai 1 * , S. Broumi 2 , Florentin Smarandache 3 , P.K.Santhi 4
Doi: https://doi.org/10.54216/JNFS.020205
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.
Neutrosophic set, neutrosophic graph, neutrosophic equitable dominating set, neutrosophic equi-table degree, neutrosophic equitable independent set.
[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.