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Title

Secure Edge Domination in Neutrosophic Graphs

  Sivasankar S 1 * ,   Said Broumi 2

1  Department of Mathematics, RV Institute of Technology and Management, Bangalore
    (sivshankar@gmail.com)

2  Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco
    (broumisaid78@gmail.com)


Doi   :   https://doi.org/10.54216/JNFS.030201

Received: March 12, 2022 Accepted: June 22, 2022

Abstract :

The concepts of Neutrosophic secure edge domination number and neutrosophic total secure edge domination number in single valued neutrosophic graphs (SVNG) with strong arcs are introduced and analysed in this paper, and some of their properties are studied. The relationship between the neutrosophic secure edge dominance number  and its inverse  is presented. The concepts inverse neutrosophic total edge domination set and inverse neutrosophic total edge domination number are also defined. Some of these concepts' properties are investigated.

Keywords :

Edge dominating set , Neutrosophic secure edge dominating number , inverse neutrosophic edge domination number

References :

[1] Akram, M. Bipolar fuzzy graphs. Information sciences, 181, 24, pp. 5548-5564, 2011.

[2] Atanassov.K.T., Intuitionistic fuzzy sets: Theory and applications, Studies in fuzziness and soft

computing, Heidelberg, New York, Physica-Verl.,1999.

[3] S. Arumugam and S. Velammal, Edge domination in graphs, Taiwanese Journal of Mathematics, 2(2)

(1998), 173-179.

[4] Berge, C. Graphs and hypergraphs, North Holland Amsterdam 1973.

[5] Broumi, S.; Nagarajan, D.; Bakali, A.; Talea, M.; Smarandache, F.; Lathamaheswari, M. The shortest

path problem in interval valued trapezoidal and triangular neutrosophic environment. Complex Intell.

Syst. 2019.

[6] Broumi, S., Smarandache, F., Talea, M. and Bakali, A. Single valued neutrosophic graphs: degree, order

and size. IEEE international conference on fuzzy systems, pp. 2444-2451,2016.

[7] G.J. Chang, Algorithmic aspects of domination in graphs, in: D.Z. Du, P.M. Pardalos (Eds.), Handbook

of Combinatorial Optimization, Vol. 3, Kluwer, Boston, MA, (1998), 339-405.

[8] Hussain, S. S., Hussain, R., and Smarandache, F. Domination number in neutrosophic soft

graphs. Neutrosophic Sets and Systems, 28, pp. 228-244, (2019).

[9] Kandasamy Vasantha, K. Ilanthenral, and Florentin Smarandache. Neutrosophic graphs: a new

dimension to graph theory. Infinite Study, 2015.

[10] M.G.Karunambigai, S.Sivasankar and K.Palanivel, Different types of Domination in Intuitionistic Fuzzy

Graph, Annals of Pure and Applied Mathematics, 14(1)(2017), 87-101.

[11] M.G.Karunambigai, S.Sivasankar and K.Palanivel, Secure domination in fuzzy graphs and intuitionistic

fuzzy graphs, Annals of Fuzzy Mathematics and Informatics, 14(1)(2017), 419-431.

[12] M.G.Karunambigai, S.Sivasankar and K.Palanivel, Secure edge domination in intuitionistic fuzzy

graphs, International Journal of Mathematics Achieve, 9(1)(2018), 190-196.

[13] V.R. Kulli, Secure and Inverse Secure Total Edge Domination and Some Secure and Inverse Secure

Fuzzy Domination Parameters, International Journal of Fuzzy Mathematical Archive, 11(1)(2016),

25-30.

[14] Merouane, H. B. and Chellali, M. On secure domination in graphs, Information Processing Letters, 115,

pp. 786-790, 2015.

[15] Nagoorgani, A and Chandrasekaran, V. T. Domination in fuzzy graph, Advances in fuzzy sets and

systems, 1, pp.17-26, 2006.

[16] Nagoorgani, A and Prasanna Devi, Edge Domination and independence in fuzzy graph, Advances in

fuzzy sets and systems, 15, pp.73-84, 2013.

[17] Ore, O. Theory of graphs, American Mathematical Society Colloquium Publications, 38, 1962.

[18] R.Parvathi and M.G. Karunambigai, Intuitionistic Fuzzy Graphs, Computational Intelligence, Theory

and applications, (2006), 139-150.

[19] R. Parvathi and G. Thamizhendhi, Domination in intuitionistic fuzzy graphs, Notes on Intuitionistic

Fuzzy Sets 16 (2010), 39-49.

[20] A. Somasundaram and S. Somasundaram. Domination in fuzzy graphs-I. Pattern Recognition Letters

19(9) (1998), 787-791.

[21] N. Vinodkumar and G. Geetharamani, Vertex edge domination in operations of fuzzy graphs,

International Journal of Advanced Engineering Technology, 7(2)(2016), 401-404.

[22] Rosenfeld, A. Fuzzy graphs: Fuzzy sets and their applications to cognitive and decision processes.

Academic press, pp. 77-95, 1975.

[23] Zadeh, L.A.: Fuzzy sets, Information and Control 8, pp. 338-353, 1965.


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MLA Sivasankar S, Said Broumi. "Secure Edge Domination in Neutrosophic Graphs." Full Length Article, Vol. 3, No. 2, 2022 ,PP. 08-18 (Doi   :  https://doi.org/10.54216/JNFS.030201)
APA Sivasankar S, Said Broumi. (2022). Secure Edge Domination in Neutrosophic Graphs. Journal of Full Length Article, 3 ( 2 ), 08-18 (Doi   :  https://doi.org/10.54216/JNFS.030201)
Chicago Sivasankar S, Said Broumi. "Secure Edge Domination in Neutrosophic Graphs." Journal of Full Length Article, 3 no. 2 (2022): 08-18 (Doi   :  https://doi.org/10.54216/JNFS.030201)
Harvard Sivasankar S, Said Broumi. (2022). Secure Edge Domination in Neutrosophic Graphs. Journal of Full Length Article, 3 ( 2 ), 08-18 (Doi   :  https://doi.org/10.54216/JNFS.030201)
Vancouver Sivasankar S, Said Broumi. Secure Edge Domination in Neutrosophic Graphs. Journal of Full Length Article, (2022); 3 ( 2 ): 08-18 (Doi   :  https://doi.org/10.54216/JNFS.030201)
IEEE Sivasankar S, Said Broumi, Secure Edge Domination in Neutrosophic Graphs, Journal of Full Length Article, Vol. 3 , No. 2 , (2022) : 08-18 (Doi   :  https://doi.org/10.54216/JNFS.030201)