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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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Continuous publication

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Open access · Articles freely available online · APC applies after acceptance

International Journal of Neutrosophic Science
Full Length Article

Inverse Dominating Set in Neutrosophic Graphs

MullaiMurugappan *
* Corresponding Author.

Abstract

In this paper, the concept of inverse domination in neutrosophic graph is established. The definition of inverse domination number, inverse dominating set, inverse split and non split dominating sets in neutrosophic graph are developed with suitable examples here. Also, the theorems in inverse domination in neutrosophic graph and the bound on inverse domination number in neutrosophic graph are derived.

Keywords

Neutrosophic graph Inverse dominating set Inverse dominating number Neutrosophic path Minimum dominating set.

References

[1] K. Ameenal Bibi and R. Selvakumar The inverse split and non-split domination in graphs.

[2] K.Atanassov, Intuitionistic fuzzy sets: Theory and applications.Physica, New York, 1999.

[3] K.Atanassov,(1986) Intuitionistic fuzzy sets Fuzzy sets and Systems, vol.20, p. 87-96.

[4] K.R. Bhutani on automorphism of fuzzy graphs.Pattern Recognition Letters 9(1989),159-162.

[5] G.J. Chang,(1998).Algorithmic aspects of domination in graphs,in D.Z. Du, P.M. Paradalos(Eds.),Handbook of combinatorial Optimization,Vol.3,Kluwer,Boston, MA, 339-405.

[6] G.S. Domke,J.E. Donbar and L.R. Markus,The inverse domination number of a graph, ARS combinatoria 72(2004)149-160

[7] S.Geetha and C.V.R. Harinarayanan, Inverse split domination in fuzzy graphs, International Journal of Engineering Research and Applications, Vol.4, Issue6(Version.2), June 2014, pp.118-121.

[8] S. Ghobadi,N.D. Soner and Q.M. Mahyoub Inverse dominating set in fuzzy graphs.

[9] P.J. Jayalakshmi 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).

[10] M.G.Karunambigai, S.Sivasankar and K.Palanivel, Edge regular intuitionistic fuzzy graph, Advances in Fuzzy sets and systems, 20(1),25-46, 2015.

[11] A. Kaufmann,introduction `a la th´eorie des sous-ensembles flous,loEl´ements th´eoriques de base.paris: Masson et Cie;(1976).

[12] V.R. Kulli and L.S.C. Sigarkanti,Inverse domination in graphs,Nat.Acad.Sci.Ltt. 14(1991) 473-475.

[13] Q.M. Mahyoub and N.D. Soner,fuzzy covering and fuzzy neighborhood set in fuzzy graphs,The split domination number of fuzzy graphs,Journal of Ultra Scientist of Physical Sciences,Vol.19,No 3M, (2007).

[14] M.L.N. McAlester, fuzzy intersection graphs.Comp. Math. Appl. 15(10)(1989),871-886.

[15] J.N. Mordeson, fuzzy line graphs.Pattern Recognition Letters,14(1993) 381-384.

[16] J.N. Mordeson and P.S. Nair,fuzzy graphs and fuzzy hyper graphs, physicaverlag,Heidelberg,(2000).

[17] M.Mullai., Domination in Neutrosophic Graphs, IGI Global Publications(Communicated).

[18] A. NagoorGani. A and S. Shajitha Begum, (2010). Degree, Order and Size in Intuitionistic Fuzzy Graph, International Journal of Algorithms,Computing and Mathematics, (3)3.

[19] Parvathi, R., and Tamizhendhi, G., Domination in intuitionistic fuzzy graphs, Foueteenth Int. Conf. on IFSs, Sofia, NIFS Vol.16, 2, 39-49, 15-16, May 2010.

[20] A. Rosenfeld,fuzzy graphs In:L.A. Zadeh,K.S.Fu and M. Shimura (Eds),Fuzzy sets and Their Applications.Academic Press,New York,(1975)

[21] Said et al (2016).Single valued neutrosophic graphs. Journal of new Theory, 10, 86-101.

[22] F.Smarandache,(2006) Neutrosophic set - a generalization of the intuitionistic fuzzy set, Granular Computing, IEEE International Conference, 3842,2006, DOI: 10.1109/ GRC.2006.1635754.

[23] F. Smarandache,(2011).A geometric interpretation of the neutrosophic set A generalization of the intuitionistic fuzzy set Granular computing (GRC),2011 IEEE International Conference, 602 606.DOI 10.1109/GRC.2011.6122665.

[24] F.Smarandache,(2015).Types of Neutrosophic Graphs and neutrosophic Algebraic Structures together with their Applications in Technology,seminar, Universitatea din Brasov, Facultatea de Design de Produs si Mediu, Brasov, Romania.

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

[26] A.Somasundaram,S.Somasundaram,Domination in fuzzy graphs-I, Pattern Recognition Letters,19(1998)787-791.

[27] A.Somasundaram,Domination in fuzzy graph-II,Journal of Fuzzy Mathematics, 20(2004).

[28] W.B.Vasantha Kandasamy, K.Ilanthenral and Florentin Smaradache, (2015).Neutrosophic Graphs: A New Dimension to Graph Theory, Kindle Edition,. [29] L.A.Zadeh, Similarity relations and fuzzy ordering, Information sciences, 3(2)(1971), 177-200

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, MullaiMurugappan. "Inverse Dominating Set in Neutrosophic Graphs." International Journal of Neutrosophic Science, vol. , no. , , pp. . DOI:
, M. (). Inverse Dominating Set in Neutrosophic Graphs. International Journal of Neutrosophic Science, (), . DOI:
, MullaiMurugappan. "Inverse Dominating Set in Neutrosophic Graphs." International Journal of Neutrosophic Science , no. (): . DOI:
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