An Introduction to Bipolar Single Valued Neutrosophic Graph Theory


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In this paper, we first define the concept of bipolar single neutrosophic graphs as the generalization of bipolar fuzzy graphs, N-graphs, intuitionistic fuzzy graph, single valued neutrosophic graphs and bipolar intuitionistic fuzzy graphs.



Edited by:

Prof.univ. Adrian Olaru






S. Broumi et al., "An Introduction to Bipolar Single Valued Neutrosophic Graph Theory", Applied Mechanics and Materials, Vol. 841, pp. 184-191, 2016

Online since:

June 2016




[1] D. Ezhilmaran & K. Sankar: Morphism of bipolar intuitionistic fuzzy graphs, in: Journal of Discrete Mathematical Sciences and Cryptography, 18: 5, 605-621 (2015), DOI: 10. 1080/ 09720529. 2015. 1013673.

DOI: 10.1080/09720529.2015.1013673

[2] F. Smarandache: Refined Literal Indeterminacy and the Multiplication Law of Sub-Indeterminacies, in: Neutrosophic Sets and Systems, Vol. 9, 58-69 (2015).

[3] F. Smarandache: Neutrosophic set - a generalization of the intuitionistic fuzzy set, Granular Computing, 2006 IEEE International Conference, 38 – 42 (2006), DOI: 10. 1109/GRC. 2006. 1635754.

DOI: 10.1109/grc.2006.1635754

[4] F. Smarandache: Types of Neutrosophic Graphs and Neutrosophic Algebraic Structures together with their Applications in Technology, seminar, Universitatea Transilvania din Brasov, Facultatea de Design de Produs si Mediu, Brasov, Romania 06 June (2015).

[5] F. Smarandache: Symbolic Neutrosophic Theory (Europanova asbl, Brussels, 195 p., Belgium 2015).

[6] H. Wang, F. Smarandache, Y. Zhang, and R. Sunderraman: Single valued Neutrosophic Sets, in: Multispace and Multistructure 4, 410-413 (2010).

[7] I. Deli, M. Ali, F. Smarandache: Bipolar neutrosophic sets and their application based on multi-criteria decision making problems, in: Advanced Mechatronic Systems (ICAMechS), 249- 254 (2015), DOI: 10. 1109/ICAMechS. 2015. 7287068.

DOI: 10.1109/icamechs.2015.7287068

[8] K. Atanassov: Intuitionistic fuzzy sets, in: Fuzzy Sets and Systems, vol. 20, 87-96 (1986).

DOI: 10.1016/s0165-0114(86)80034-3

[9] L. Zadeh: Fuzzy sets, in: Inform and Control, 8, 338-353 (1965).

[10] M. Akram and B. Davvaz: Strong intuitionistic fuzzy graphs, in: Filomat, vol. 26, no. 1, 177–196 (2012).

DOI: 10.2298/fil1201177a

[11] M. Akram: Bipolar fuzzy graphs, in: Information Sciences, vol. 181, no. 24, 5548–5564 (2011).

DOI: 10.1016/j.ins.2011.07.037

[12] M. Akram: Bipolar fuzzy graphs with applications, in: Knowledge Based Systems, vol. 39, 1–8 (2013).

[13] M. Akram, K. H. Dar: On N- graphs, in: Southeast Asian Bulletin of Mathematics (2012).

[14] M. Akram, W. A. Dudek: Regular bipolar fuzzy graphs, in: Neural Computing and Applications, Vol 21, 197-205 (2012).

DOI: 10.1007/s00521-011-0772-6

[15] P. Bhattacharya: Some remarks on fuzzy graphs, in: Pattern Recognition Letters 6: 297-302 (1987).

[16] R. Parvathi and M. G. Karunambigai: Intuitionistic Fuzzy Graphs, Computational Intelligence, Theory and applications, International Conference in Germany, Sept 18-20 (2006).

DOI: 10.1007/3-540-34783-6_15

[17] S. Broumi, M. Talea, F. Smarandache: Single Valued Neutrosophic Graphs: Degree, Order and Size, (2016) submitted.

DOI: 10.1109/fuzz-ieee.2016.7738000

[18] S. Broumi, M. Talea. A. Bakkali and F. Smarandache: Single Valued Neutrosophic Graph, in: Journal of New Theory, N 10, 68-101 (2016).

DOI: 10.4028/

[19] W. B. Vasantha Kandasamy and F. Smarandache: Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps (USA, 2013).

[20] W. B. Vasantha Kandasamy, K. Ilanthenral and Florentin Smarandache: Neutrosophic Graphs: A New Dimension to Graph Theory (Kindle Edition, 2015).

[21] W.B. Vasantha Kandasamy and F. Smarandache: Analysis of social aspects of migrant laborers living with HIV/AIDS using Fuzzy Theory and Neutrosophic Cognitive Maps (Xiquan, Phoenix, USA, 2004).

[22] More information on http: /fs. gallup. unm. edu/NSS.

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