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International Journal of Neutrosophic Science
Volume 0 - 2019 , Issue I - Vol 0, PP: 08-20 , 2019 | Cite this article as | XML | Html |PDF

Title

Homomorphism and Isomorphism in strong neutrosophic graphs

  M. Mulla 1 * ,   Said Broumi 2 ,   R.Jeyabalan 3

1  Department of Mathematics, Alagappa University, Karaikudi, Tamilnadu, India
    (mullaim@alagappauniversity.ac.in)

2  Laboratory of Information processing, University Hassan II,B.P 7955, Sidi Othman, Casablanca, Morocco
    (broumisaid78@gmail.com)

3  Department of Mathematics, Alagappa University, Karaikudi, Tamilnadu, India
    (jeyram84@gmail.com)


Doi   :   https://doi.org/10.54216/IJNS.000101

Received: January 14, 2019 Revised: March 27, 2019 Accepted: April 28, 2019

Abstract :

The concept of strong neutrosophic graph is developed with example and some of their properties are investigated in this paper. Some definitions, homomorphism, isomorphism theorems and propositions in strong neutrosophic graphs are established. Basic operations (like union, intersection etc.,) and complement of strong neutrosophic graphs are also derived here.

Keywords :

Strong neutrosophic graph , Complete neutrosophic graph , Complement of a neutrosophic graph , Cartesian product , Isomorphism

References :

[1] A.Alaoui, On fuzzification of some concepts of graphs , Fuzzy Sets and Systems 101,363-389, 1999.

[2] K.T.Atanassov, Intuitionistic fuzzy sets : Theory,applications,Studies in fuzziness and soft computing, Heidelberg,Newyork,physica-verl.,1999.

[3] K.T.Atanassov, Intuitionistic fuzzy sets,Fuzzy Sets and Systems, 20,1986.

[4] P.Bhattacharya, Some remarks on fuzzy graphs, Pattern Recognition Letters, 6, pp.297-302,1987.

[5] K.R. Bhuttani, On automorphisms of fuzzy graphs, Pattern Recognition Letters, 9, pp.159-162,1987.

[6] K.R. Bhuttani, A Rosenfield, Strong arcs in fuzzy graphs, Information Sciences, 152, pp.319-322,2003.

[7] Euler, Leonhard ,"Solutio problematis ad geometriam situs pertinentis", Comment. Acad. Sci. U. Petrop 8, pp.128–40,1736.

[8] K.P.Huber M.R.Berthold, Application of fuzzy graphs formet a modeling, Proceedings of the 2002 IEEE

Conference,pp.640-644.

[9] A. Kiss, “An application of fuzzy graphs in database theory”, Pure Mathematics and Applications 1, pp.337- 342, 1991.

[10] S. Mathew, M.S. Sunitha, “Types of arcs in a fuzzy graph”, Information Sciences, 179, pp.1760-1768,2009.

[11] S. Mathew, M.S. Sunitha, “Node connectivity, arc connectivity of a fuzzy graph”, Information Sciences, 180, pp.519-531,2010.

[12] J.N.mordeson,P.S.Nair, “Fuzzy Graphs and Fuzzy Hypergraphs”,physica, verlag,Heidelberg,2000.

[13] J.N.Mordeson,C.S Peng,”Operations on fuzzy graphs”,Information Sciences 79, pp.159-170, 1994.

[14] J.N.Moderson, “Fuzzy line graphs”,Pattern Recognition Letters, 14, pp.381-384,1993.

[15] G. Pasi, R. Yager, K.T. Atanassov, “Intuitionistic fuzzy graph interpretations of multi-person multi-criteria decision making: generalized net approach”, Intelligent Systems. Proceedings. 2004 2nd International IEEE Conference, pp.434-439, 2004.

[16] R. Parvathi, M.G. Karunambigai, “Intuitionistic fuzzy graphs”, Journal of computational Intelligence: Theory and Applications, pp.139-150,2006.

[17] R. Parvathi, M.G. Karunambigai, K.T. Atanassov, “Operations on intuitionistic fuzzy graphs”, Fuzzy Systems, 2009. FUZZ-IEEE 2009. IEEE International Conference, pp.1396-1401, 2009.

[18] A. Rosenfield, “fuzzy graphs”,in: L.A.Zadeh,K.S.Fu,K.Tanaka,M.Shimura(Eds.), Fuzzy Sets and Their

Applications to Cognitive and Decision Processes,Academic Press, New York, pp.77-95,1975.

[19] Said et al (2016). “Single valued neutrosophic graphs”,Journal of New Theory,10, 86-101,2016.

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

[21] F. Smarandache,”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.

[22] F.Smarandache,”Symbolic Neutrosophic Theory”, Europanovaasbl, Brussels, 195p, 2015.

[23] M.Mullai, “Domination in neutrosophic graphs”, Neutrosophic Graph Theory and Algorithms, IGI Global Publications,pp.131-147, 2019.


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MLA M. Mulla, Said Broumi, R.Jeyabalan. "Homomorphism and Isomorphism in strong neutrosophic graphs." International Journal of Neutrosophic Science, Vol. 0 - 2019, No. I - Vol 0, 2019 ,PP. 08-20 (Doi   :  https://doi.org/10.54216/IJNS.000101)
APA M. Mulla, Said Broumi, R.Jeyabalan. (2019). Homomorphism and Isomorphism in strong neutrosophic graphs. Journal of International Journal of Neutrosophic Science, 0 - 2019 ( I - Vol 0 ), 08-20 (Doi   :  https://doi.org/10.54216/IJNS.000101)
Chicago M. Mulla, Said Broumi, R.Jeyabalan. "Homomorphism and Isomorphism in strong neutrosophic graphs." Journal of International Journal of Neutrosophic Science, 0 - 2019 no. I - Vol 0 (2019): 08-20 (Doi   :  https://doi.org/10.54216/IJNS.000101)
Harvard M. Mulla, Said Broumi, R.Jeyabalan. (2019). Homomorphism and Isomorphism in strong neutrosophic graphs. Journal of International Journal of Neutrosophic Science, 0 - 2019 ( I - Vol 0 ), 08-20 (Doi   :  https://doi.org/10.54216/IJNS.000101)
Vancouver M. Mulla, Said Broumi, R.Jeyabalan. Homomorphism and Isomorphism in strong neutrosophic graphs. Journal of International Journal of Neutrosophic Science, (2019); 0 - 2019 ( I - Vol 0 ): 08-20 (Doi   :  https://doi.org/10.54216/IJNS.000101)
IEEE M. Mulla, Said Broumi, R.Jeyabalan, Homomorphism and Isomorphism in strong neutrosophic graphs, Journal of International Journal of Neutrosophic Science, Vol. 0 - 2019 , No. I - Vol 0 , (2019) : 08-20 (Doi   :  https://doi.org/10.54216/IJNS.000101)