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SINGLE-VALUED NEUTROSOPHIC LINE GRAPHS

Yıl 2018, Cilt: 8 Sayı: 2, 483 - 494, 01.12.2018

Öz

In this paper, the concept of a single-valued neutrosophic line graph SVNLG of a single-valued neutrosophic graph SVNG is introduced and its properties are inves- tigated. We state a necessary and sucient condition for a SVNG to be isomorphic to its corresponding SVNLG. Moreover, a necessary and sucient condition for a SVNG to be the SVNLG of some SVNG is given. The notion of a single-valued neutrosophic clique SVNC is introduced. A complete characterization of the structure of the SVNC is presented.

Kaynakça

  • Akram, M. and Davvaz, B., (2012), Strong intuitionistic fuzzy graphs, Filomat, 26 (1), pp. 177-196.
  • Akram, M. and Shahzadi, S., (2017), Neutrosophic soft graphs with application, Journal of Intelligent and Fuzzy Systems, 32 (1), pp. 841-858.
  • Akram, M. and Naz, S., (2018), Energy of Pythagorean fuzzy graphs with applications, Mathematics, (8), pp. 1-27.
  • Ashraf, S., Naz, S., Rashmanlou, H. and Malik, M. A., (2017), Regularity of graphs in single-valued neutrosophic environment, Journal of Intelligent and Fuzzy Systems, 33(1), pp. 529-542.
  • Atanassov, K. T., (1986), Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1), pp. 87-96.
  • Atanassov, K. and Gargov, G., (1989), Interval-valued intuitionistic fuzzy sets, Fuzzy Sets Syst., 31 (3), pp. 343-349.
  • Bhattacharya, P., (1987), Some remarks on fuzzy graphs, Pattern Recognition Letters, 6 (5), pp. 302.
  • Broumi, S., Talea, M., Bakali, A. and Smarandache, F., (2016), Single-valued neutrosophic graphs
  • Journal of new theory, pp. 86-101. Dhavaseelan, R., Vikramaprasad, R. and Krishnaraj. V., (2015), Certain types of neutrosophic graphs
  • Int. J. of Mathematical Sciences and Applications, 5 (2), pp. 333-339. Harary, F., (1972) Graph Theory, 3rd Edition, Addison-Wesley, Reading, MA.
  • Kaufmann, A., (1973), Introduction a la Theorie des Sour-ensembles Flous, Masson et Cie 1.
  • Mordeson, J. N., (1993), Fuzzy line graphs, Pattern Recognition Letters, 14, pp. 381-384.
  • Nair, P. S. and Cheng, S-C. Cliques and fuzzy cliques in fuzzy graphs, IEEE 2001.
  • Naz, S., Rashmanlou, H. and Malik, M. A., (2017), Operations on single-valued neutrosophic graphs with application, Journal of Intelligent and Fuzzy Systems, 32(3), pp. 2137-2151.
  • Naz, S., Akram, M. and Smarandache, F., (2018), Certain notions of energy in single-valued neutro- sophic graphs, Axioms, 7(3), pp. 1-30.
  • Naz, S., Malik, M. A. and Rashmanlou, H., (2018), Hypergraphs and transversals of hypergraphs in interval-valued intuitionistic fuzzy setting, The Journal of Multiple-Valued Logic and Soft Computing, (4-6), PP. 399-417.
  • Naz, S., Ashraf, S. and Akram, M., (2018), A novel approach to decision-making with Pythagorean fuzzy information, Mathematics, 6(6), pp. 1-28.
  • Rosenfeld, A., (1975), Fuzzy graphs, Fuzzy Sets and their Applications (L. A. Zadeh, K. S. Fu, M. Shimura, Eds.) Academic Press, New York, pp. 77-95.
  • Sahoo, S. and Pal, M., (2015), Intuitionistic fuzzy competition graphs, J. Appl. Math. Comput., 52 (1), pp. 37-57.
  • Sahoo, S. and Pal, M., (2017), Intuitionistic fuzzy tolerance graph with application, Journal of Applied
  • Mathematics and Computing, 55 (1-2), pp. 495-511. Smarandache, F., A unifying field in logics. Neutrosophy: neutrosophic probability, set and logic, American Research Press, Rehoboth, 1999.
  • Vasantha Kandasamy, W. B., Ilanthenral, K. and Smarandache, F., (2015), Neutrosophic Graphs: A
  • New Dimension to Graph Theory, kindle Edition. Wang, H., Smarandache, F., Zhang, Y. Q. and Sunderraman, R., (2010), Single-valued neutrosophic sets, Multispace and Multistructure, 4, pp. 410-413.
  • Yang, H. L., Guo, Z. L., She, Y. and Liao, X., (2016), On single-valued neutrosophic relations, Journal of Intelligent and Fuzzy Systems, 30, pp. 1045-1056.
  • Zadeh, L. A., (1965), Fuzzy sets, Information and Control, 8(3), pp. 338-353.
Yıl 2018, Cilt: 8 Sayı: 2, 483 - 494, 01.12.2018

Öz

Kaynakça

  • Akram, M. and Davvaz, B., (2012), Strong intuitionistic fuzzy graphs, Filomat, 26 (1), pp. 177-196.
  • Akram, M. and Shahzadi, S., (2017), Neutrosophic soft graphs with application, Journal of Intelligent and Fuzzy Systems, 32 (1), pp. 841-858.
  • Akram, M. and Naz, S., (2018), Energy of Pythagorean fuzzy graphs with applications, Mathematics, (8), pp. 1-27.
  • Ashraf, S., Naz, S., Rashmanlou, H. and Malik, M. A., (2017), Regularity of graphs in single-valued neutrosophic environment, Journal of Intelligent and Fuzzy Systems, 33(1), pp. 529-542.
  • Atanassov, K. T., (1986), Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1), pp. 87-96.
  • Atanassov, K. and Gargov, G., (1989), Interval-valued intuitionistic fuzzy sets, Fuzzy Sets Syst., 31 (3), pp. 343-349.
  • Bhattacharya, P., (1987), Some remarks on fuzzy graphs, Pattern Recognition Letters, 6 (5), pp. 302.
  • Broumi, S., Talea, M., Bakali, A. and Smarandache, F., (2016), Single-valued neutrosophic graphs
  • Journal of new theory, pp. 86-101. Dhavaseelan, R., Vikramaprasad, R. and Krishnaraj. V., (2015), Certain types of neutrosophic graphs
  • Int. J. of Mathematical Sciences and Applications, 5 (2), pp. 333-339. Harary, F., (1972) Graph Theory, 3rd Edition, Addison-Wesley, Reading, MA.
  • Kaufmann, A., (1973), Introduction a la Theorie des Sour-ensembles Flous, Masson et Cie 1.
  • Mordeson, J. N., (1993), Fuzzy line graphs, Pattern Recognition Letters, 14, pp. 381-384.
  • Nair, P. S. and Cheng, S-C. Cliques and fuzzy cliques in fuzzy graphs, IEEE 2001.
  • Naz, S., Rashmanlou, H. and Malik, M. A., (2017), Operations on single-valued neutrosophic graphs with application, Journal of Intelligent and Fuzzy Systems, 32(3), pp. 2137-2151.
  • Naz, S., Akram, M. and Smarandache, F., (2018), Certain notions of energy in single-valued neutro- sophic graphs, Axioms, 7(3), pp. 1-30.
  • Naz, S., Malik, M. A. and Rashmanlou, H., (2018), Hypergraphs and transversals of hypergraphs in interval-valued intuitionistic fuzzy setting, The Journal of Multiple-Valued Logic and Soft Computing, (4-6), PP. 399-417.
  • Naz, S., Ashraf, S. and Akram, M., (2018), A novel approach to decision-making with Pythagorean fuzzy information, Mathematics, 6(6), pp. 1-28.
  • Rosenfeld, A., (1975), Fuzzy graphs, Fuzzy Sets and their Applications (L. A. Zadeh, K. S. Fu, M. Shimura, Eds.) Academic Press, New York, pp. 77-95.
  • Sahoo, S. and Pal, M., (2015), Intuitionistic fuzzy competition graphs, J. Appl. Math. Comput., 52 (1), pp. 37-57.
  • Sahoo, S. and Pal, M., (2017), Intuitionistic fuzzy tolerance graph with application, Journal of Applied
  • Mathematics and Computing, 55 (1-2), pp. 495-511. Smarandache, F., A unifying field in logics. Neutrosophy: neutrosophic probability, set and logic, American Research Press, Rehoboth, 1999.
  • Vasantha Kandasamy, W. B., Ilanthenral, K. and Smarandache, F., (2015), Neutrosophic Graphs: A
  • New Dimension to Graph Theory, kindle Edition. Wang, H., Smarandache, F., Zhang, Y. Q. and Sunderraman, R., (2010), Single-valued neutrosophic sets, Multispace and Multistructure, 4, pp. 410-413.
  • Yang, H. L., Guo, Z. L., She, Y. and Liao, X., (2016), On single-valued neutrosophic relations, Journal of Intelligent and Fuzzy Systems, 30, pp. 1045-1056.
  • Zadeh, L. A., (1965), Fuzzy sets, Information and Control, 8(3), pp. 338-353.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

S. Naz Bu kişi benim

M. A. Malik Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 8 Sayı: 2

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