Secure Edge Domination in Neutrosophic Graphs

Sivasankar; Said

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

Full Length Article

Volume 3 • Issue 2 • PP: 08-18 • 2022

Secure Edge Domination in Neutrosophic Graphs

Sivasankar S ^1*

mail

,

Said Broumi ²

mail

¹Department of Mathematics, RV Institute of Technology and Management, Bangalore

²Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco

* Corresponding Author.

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

format_quote Cite this article

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

View PDF open_in_new

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.

Cite This Article

Choose your preferred format

format_quote

S, Sivasankar, Broumi, Said. "Secure Edge Domination in Neutrosophic Graphs." Journal of Neutrosophic and Fuzzy Systems, vol. Volume 3, no. Issue 2, 2022, pp. 08-18. DOI: https://doi.org/10.54216/JNFS.030201

S, S., Broumi, S. (2022). Secure Edge Domination in Neutrosophic Graphs. Journal of Neutrosophic and Fuzzy Systems, Volume 3(Issue 2), 08-18. DOI: https://doi.org/10.54216/JNFS.030201

S, Sivasankar, Broumi, Said. "Secure Edge Domination in Neutrosophic Graphs." Journal of Neutrosophic and Fuzzy Systems Volume 3, no. Issue 2 (2022): 08-18. DOI: https://doi.org/10.54216/JNFS.030201

S, S., Broumi, S. (2022) 'Secure Edge Domination in Neutrosophic Graphs', Journal of Neutrosophic and Fuzzy Systems, Volume 3(Issue 2), pp. 08-18. DOI: https://doi.org/10.54216/JNFS.030201

S S, Broumi S. Secure Edge Domination in Neutrosophic Graphs. Journal of Neutrosophic and Fuzzy Systems. 2022;Volume 3(Issue 2):08-18. DOI: https://doi.org/10.54216/JNFS.030201

S. S, S. Broumi, "Secure Edge Domination in Neutrosophic Graphs," Journal of Neutrosophic and Fuzzy Systems, vol. Volume 3, no. Issue 2, pp. 08-18, 2022. DOI: https://doi.org/10.54216/JNFS.030201

Digital Archive Ready