277 199
Full Length Article
International Journal of Neutrosophic Science
Volume 16 , Issue 1, PP: 16-27 , 2021 | Cite this article as | XML | Html |PDF

Title

More on Single Valued Neutrosophic R-dynamic Vertex Coloring and R-dynamic Edge Coloring of graphs

Authors Names :   Aparna V   1 *     Mohanapriya N   2     Broumi Said   3  

1  Affiliation :  PG and Research Department of Mathematics, Kongunadu Arts and Science College, Coimbatore-641 029, Tamil Nadu, India

    Email :  aparnav18794@gmail.com


2  Affiliation :  PG and Research Department of Mathematics, Kongunadu Arts and Science College, Coimbatore-641 029, Tamil Nadu, India

    Email :  phdmohana@gmail.com


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

    Email :  broumisaid78@gmail.com



Doi   :   https://doi.org/10.54216/IJNS.160102

Received: June 07, 2021 Accepted: October 19, 2021

Abstract :

The notion of neutrosophic sets facilitates the analysis of values that are unclear or indeterminate. In thispaper, we discuss the single valued neutrosophic R-dynamic vertex coloring of Cartesian product of SVNG’sand join of SVNG’s. Further we have described the concept of single valued neutrosophic R-dynamic edgecoloring and provided some examples and theorems.

Keywords :

Single Valued Neutrosophic Graph; Single Valued Neutrosophic Vertex Coloring; Single Valued Neutrosophic R-dynamic Vertex Coloring; Single Valued Neutrosophic Edge Coloring; Single Valued Neutrosophic R-dynamic Edge Coloring

References :

[1] M. Akram, S. Siddique and B. Davvaz, ”New concepts in neutrosophic graphs with application”, Journal of Applied Mathematics and Computing, 57, pp.279-302, 2018.

[2] M. Akram and S. Shahzadi, ”Neutrosophic soft graphs with application”, Journal of Intelligent and FuzzySystems, 32(1), pp.841-858, 2017.

[3] M. Akram and S. Shahzadi, ”Operations on single-valued neutrosophic graphs”, Journal of UncertainSystems, 11, pp.1-26, 2016.

[4] Anjaly Kishore and M. S. Sunitha, ”Strong chromatic number of fuzzy graphs, Annals of Pure and Applied Mathematics, 7(2), pp.52-60, 2014.

[5] V. Aparna, N. Mohanapriya and Said Broumi, ”Single Valued Neutrosophic R-dynamic Vertex Coloring of graphs”(Accepted).

[6] Arindam Dey and Anita Pal, ”Vertex Coloring of a Fuzzy Graph using Alpa Cut”, International Journal of Management, IT and Engineering, 2(8), pp.340-352, 2012.

[7] K. T. Atanassov, ”Intuitionistic fuzzy sets”, Fuzzy sets and systems, 20, pp.87-96, 1986.

[8] S. Broumi, M. Talea, M. Bakali and F. Smarandache, ”Single-valued neutrosophic graphs”, Journal of New Theory, 10, pp.86-101, 2016.

[9] S. Broumi, M. Talea, F. Smarandache and M. Bakali, ”Single valued neutrosophic graphs: Degree, Orderand Size”, IEEE International Conference on Fuzzy Systems (FUZZ), pp.2444-2451, 2016.

[10] Changiz Eslahchi and B. N. Onagh, ”Vertex strength of fuzzy graphs”, International Journal of Mathematics and Mathematical Sciences, pp.1-9, 2005.

[11] R. Dhavaseelan, R. Vikramaprasad and V. Krishnaraj, ”Certain types of neutrosophic graphs”, International Journal of Mathematical Sciences and Applications, 5(2), pp.333-339, 2015.

[12] S. Ismail Mohideen and M. A. Rifayathali, ”Coloring of Intuitionistic fuzzy graph using (α, β)-cuts”,International Research Journal of Mathematical Engineering and IT, 2, pp.14-26, 2015.

[13] S. Lavanya and R. Sattanathan, ”Fuzzy total coloring of fuzzy graph”, International Journal of InformationTechnology and Knowledge Management, 2, pp.37-39, 2009.

[14] B. Montgomery, ”Dynamic coloring of graphs”, ProQuest LLC, Ann Arbor, MI, Ph.D Thesis, West Virginia University, 2001.

[15] M. A. Rifayathali, A. Prasanna and S. Ismail Mohideen, ”Strong intuitionistic fuzzy graph coloring”,International Journal of Latest Engineering Research and Applications, 2, pp.163-169, 2017.

[16] A. Rohini, M. Venkatachalam, S. Broumi and F. Smarandache, ”Single Valued Neutrosophic Coloring”,Neutrosophic Sets and Systems, 28, pp.13-22, 2019.

[17] A. Rohini, M. Venkatachalam, Dafik, S. Broumi and F. Smarandache, ”Operations of Single ValuedNeutrosophic Coloring”, Neutrosophic Sets and Systems, 31, pp.172-178, 2020.

[18] A. Rohini, M. Venkatachalam, Dafik, S. Broumi and F. Smarandache, ”Single Valued NeutrosophicIrregular Vertex Coloring”, Acta Electrotechnica, 61, pp.56-60, 2020.

[19] A. Rosenfeld, ”Fuzzy graphs”, Fuzzy sets and their applications, Academic Press, New York, 1975.

[20] F. Smarandache, ”Neutrosophy: Neutrosophic Probability, Set and logic”, Ann Arbor, Michigan, USA, 105, 2002.

[21] Susana Munoz, M. Teresa Ortuno, Javier Ramirez and Javier Yanez, ”Coloring fuzzy graphs”, Omega,

33(3), pp.211-221, 2005.

[22] H. Wang, F. Smarandache, Y. Zhang and R. Sunderraman, ”Single-valued neutrosophic sets”, MultisspaceMultiscriot, 4, pp.410-413, 2010.

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


Cite this Article as :
Aparna V , Mohanapriya N , Broumi Said, More on Single Valued Neutrosophic R-dynamic Vertex Coloring and R-dynamic Edge Coloring of graphs, International Journal of Neutrosophic Science, Vol. 16 , No. 1 , (2021) : 16-27 (Doi   :  https://doi.org/10.54216/IJNS.160102)