Volume 0 - 2019 • Issue I - Vol 0 • PP: 08-20 • 2019
Homomorphism and Isomorphism in strong neutrosophic graphs
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© 2019 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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
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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