Bipolar Neutrosophic Graph Structures

Muhammad Akram, Muzzamal Sitara


In this research study, we introduce the concept of bipolar single-valued neutrosophic graph structures.We discuss certain notions of bipolar single-valued neutrosophic graph structures with examples.We present some methods of construction of bipolar single-valued neutrosophic graph structures.We also investigate some of their prosperities.


Graph structure, Bipolar single-valued neutrosophic graph structure, Operations

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Akram, M. (2011). Bipolar fuzzy graphs, Information Sciences, 181(24), 5548 − 5564.

Akram, M . (2016). Single-valued neutrosophic planar graphs, International Journal of Algebra and

Statistics, 5(2), 157-167.

Akram, M., and Akmal, R. (2016). Application of bipolar fuzzy sets in graph structures, Applied

Computational Intelligence and Soft Computing, 13 pages.

Akram, M., and Shahzadi, S. (2017). Neutrosophic soft graphs with application, Journal of Intelligent

& Fuzzy Systems, 32, 841-858.

Akram, M., and Shahzadi, S. (2016). Representation of graphs using intuitionistic neutrosophic soft

sets, Journal of Mathematical Analysis, 7(6), 31-53.

Atanassov, K. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1) , 87 − 96.

Bhattacharya, P. (1987). Some remarks on fuzzy graphs, Pattern Recognition Letters, 6(5), 297−302.

Broumi, S., Smarandache, F., Talea, M., and Bakali, A. (2016). An introduction to bipolar single

valued neutrosophic graph theory, Applied Mechanics and Materials, 841, 184 − 191.

Deli, I., Ali, M., and Smarandache, F. (2015). Bipolar neutrosophic sets and their application based

on multi-criteria decision making problems, arXiv preprint arXiv: 1504.02773.

Dhavaseelan, R., Vikramaprasad, R., and Krishnaraj, V. (2015). Certain types of neutrosophic

graphs, Int Jr. of Mathematical Sciences and Applications, 5(2), 333 − 339.

Dinesh, T. (2011). A study on graph structures, incidence algebras and their fuzzy ana-

logues[Ph.D.thesis], Kannur University, Kannur, India.

Dinesh, T., and Ramakrishnan, T.V. (2011). On generalised fuzzy graph structures, Applied Mathe-

matical Sciences, 5(4), 173 − 180.

Kauffman, A. (1973). Introduction a la Theorie des Sous-emsembles Flous, Masson et Cie Vol.1.

J.N. Mordeson and P. Chang-Shyh, Operations on fuzzy graphs, Information Sciences, 79, (1994)

− 170.

Peng, J.J., Wang, J.Q., Zhang, H.Y., and Chen, X.H. (2014). An outranking approach for multi-

criteria decision-making problems with simplified neutrosophic sets, Applied Soft Computing, 25,

− 346.

Rosenfeld, A. (1975). Fuzzy graphs, Fuzzy Sets and their Applications( L.A.Zadeh, K.S.Fu,

M.Shimura, Eds.), Academic Press, New York 77 − 95.

Sampathkumar, E. (2006). Generalized graph structures, Bulletin of KeralaMathematics Association,

(2), 65 − 123.

Shah, N., and Hussain, A. (2016). Neutrosophic soft graphs, Neutrosophic Set and Systems, 11,

− 44.

Smarandache, F. (1998). Neutrosophy Neutrosophic Probability, Set, and Logic, Amer Res Press,

Rehoboth, USA.

Sunitha, M.S., and Vijayakumar, A. (2002). Complement of a fuzzy graph, Indian Journal of Pure

and Applied Mathematics, 33(9), 1451 − 1464.

Wang, H., Smarandache, F., Zhang, Y.Q, and Sunderraman, R. (2010). Single valued neutrosophic

sets, Multispace and Multistructure, 4, 410 − 413.

Ye, J. (2014). Single-valued neutrosophic minimum spanning tree and its clustering method, Journal

of Intelligent Systems, 23(3), 311 − 324.

Zadeh, L.A. (1965). Fuzzy sets, Information and control, 8(3), 338 − 353.

Zadeh, L.A. (1971). Similarity relations and fuzzy orderings, Information Sciences, 3(2), 177 − 200.

Zhang, W., -R. Bipolar fuzzy sets and relations: a computational framework for cognitive modeling

and multiagent decision analysis, In Fuzzy Information Processing Society Biannual Conference,

Industrial Fuzzy Control and Intelligent systems Conference, and the NASA Joint Technology

Workshop on Neural Networks and Fuzzy Logic, 305 − 309, IEEE 1994



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