Volume 12 • Issue 1 • PP: 29-38 • 2020
Neutrosophic Vague Incidence Graph
View PDF Abstract
Vague sets gives more intuitive graphical notation of vague data, that devotes better analysis in information relationships, incompleteness and similarity measures. Neutrosophic graphs are used as a mathematical tool to kept an imprecise and unspecified information. In this paper, the neutrosophic vague incidence graphs are introduced. The edge-connectivity, vertex-connectivity and pair-connectivity in neutrosophic vague incidence graphs are established. The given results are illustrated with suitable example.
Keywords
References
[1] Ajay, D. and Chellamani, P., “Fuzzy magic labelling of Neutrosophic path and star graph”, Advances in Mathematics: Scientific Journal, Vol 9, No. 8, pp. 6059–6070, 2020.
[2] Ajay, D., Manivel, M., and Aldring, J.,“ Neutrosophic Fuzzy SAW Method and It’s Application”. The International Journal of Analytical and Experimental Modal Analysis, Vol 11, No. 8, pp. 881-887, 2019.
[3] Ajay, D. and Aldring, J., “A Decision-Making Technique Based on Similarity Measure and Entropy of Bipolar Neutrosophic Sets”, The International Journal of Analytical and Experimental Modal Analysis, Vol 11, No. 9, pp. 520-529, 2019.
[4] Ajay, D., Broumi, S. and Aldring, J., “An MCDM Method under Neutrosophic Cubic Fuzzy Sets with Geometric Bonferroni Mean Operator”, Neutrosophic Sets and Systems, Vol 32, No. 1, pp. 1-13. 2020. DOI: 10.5281/zenodo.3723621.
[5] Ajay, D., Aldring, J., Abirami, S. and Jeni Seles Martina, D., “A SVTrN-number approach of multiobjective optimisation on the basis of simple ratio analysis based on MCDM method”. International Journal of Neutrosophic Science (IJNS), Vol 5, No. 1, pp. 16-28, 2020.
[6] Akram, M. and Shahzadi, G., “Operations on single-valued neutrosophic graphs, Journal of Uncertain Systems, 11(1) (2017), 1-26.
[7] Akram, M., Sayed, S. and Smarandache, F., “Neutrosophic incidence graphs with application”, Axioms, Vol 7, No. 3, pp. 1-47, 2018
[8] Al-Quran, A. and Hassan, N., “Neutrosophic vague soft expert set theory, Journal of Intelligent & Fuzzy Systems, Vol 30, No. 6, pp. 3691-3702, 2016
[9] Al-Tahan, M. and Davvaz, B., “On Single Valued Neutrosophic Sets and Neutrosophic N-Structures: Applications on Algebraic Atructures (Hyperstructures)”, International Journal of Neutrosophic Science (IJNS), Vol 3, No. 2, pp. 108-117, 2020.
[10]Al- Tahan, M., “Some Results on Single Valued Neutrosophic (Weak) Polygroups”, International Journal of Neutrosophic Science (IJNS), Vol 2, No. 1, pp. 38-46, 2020
[11]Alkhazaleh, S., “Neutrosophic vague set theory”, Critical Review, Vol 10, pp. 29-39, 2015.
[12]Borzooei, A. R. and Rashmanlou, H., “Degree of vertices in vague graphs”, Journal of Applied Mathematics and Informatics, Vol 33, pp. 545-557, 2015.
[13]Borzooei, A. R. and Rashmanlou, H., “Domination in vague graphs and its applications”, Journal of Intelligent & Fuzzy Systems, Vol 29, pp. 1933-1940, 2015.
[14]Borzooei, A. R., Rashmanlou, H., Samanta, S. and Pal, M., “Regularity of vague graphs”, Journal of Intelligent & Fuzzy Systems, Vol 30, pp. 3681-3689, 2016.
[15]Broumi, S. and Smarandache, F., “Intuitionistic neutrosophic soft set”, Journal of Information and Computer Science, Vol 8, No. 2, pp. 130-140, 2013.
[16]Broumi, S., Smarandache, F., Talea, M. and Bakali., “Single-valued neutrosophic graphs: Degree, Order and Size”, IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2016.
[17]Broumi, S., Mohamed, T., Assia, B. and Smarandache, F., “Single-valued neutrosophic graphs”, The Journal of New Theory, Vol 2016, No. 10, pp. 861-101, 2016.
[18]Darabian, E., Borzooei, R. A., Rashmanlou, H. and Azadi, M., “New concepts of regular and (highly) irregular vague graphs with applications”, Fuzzy Information and Engineering, Vol 9, No. 2, pp. 161-179, 2017.
[19] Deli, I. and Broumi, S., “Neutrosophic soft relations and some properties”, Annals of Fuzzy Mathematics and Informatics, Vol 9, No. 1, pp. 169-182, 2014.
[20]Deli, I. and S¸ubas¸, Y., “Some weighted geometric operators with SVTrN-numbers and their application to multi-criteria decision-making problems”, Journal of Intelligent & Fuzzy Systems, Vol 32, No. 1, pp. 291-301, 2017
[21]Deli, I. and Ozt ¨ urk, E. K., “Two Centroid Point for SVTN-Numbers and SVTrN-Numbers: SVN-MADM ¨ Method”, In Neutrosophic Graph Theory and Algorithms, IGI Global, pp. 279-307, 2020.
[22]Dhavaseelan, R., Vikramaprasad, R. and Krishnaraj, V., “Certain types of neutrosophic graphs”, International Journal of Mathematical Sciences and Applications, Vol 5, No. 2, pp. 333-339, (2015).
[23]Dhavaseelan, R., Jafari, S., Farahani M. R and Broumi S, “On single-valued co-neutrosophic graphs”, Neutrosophic Sets and Systems, An International Book Series in Information Science and Engineering, Vol 22, 2018.
[24]Molodtsov D, “Soft set theory-first results”, Computers and Mathematics with Applications, Vol 37, No. 2, pp. 19-31, 1999.
[25]Muhiuddin, G. and Al-roqi, A. M., “Cubic soft sets with applications in BCK/BCI-algebras”, Annals of Fuzzy Mathematics and Informatics, Vol 8, No. 2, pp. 291-304, 2014.
[26]Muhiuddin, G., “Neutrosophic Sub semi-groups”, Annals of Communications in Mathematics, 1(1), (2018).
[27]Mordeson, J.N., “Fuzzy line graphs”, Pattern Recognition Letters, Vol 14, pp. 381-384, 1993.
[28]Hussain, S. S., Hussain, R. J. and Muhiuddin, G., “Neutrosophic Vague Line Graphs”, Neutrosophic Sets and Systems, Vol 36, pp. 121-130, 2020.
[29]Hussain, S. S., Hussain, R. J., Jun, Y. B. and Smarandache, F., “Neutrosophic bipolar vague set and its application to neutrosophic bipolar vague graphs”, Neutrosophic Sets and Systems, Vol 28, pp. 69-86, 2020.
[30]Hussain, S. S., Hussain, R. J. and Smarandache, F., “On neutrosophic vague graphs”, Neutrosophic Sets and Systems, Vol 28, pp. 245-258, 2019.
[31]Hussain, S. S., Broumi, S., Jun, Y. B. and Durga, N., “Intuitionistic bipolar neutrosophic set and its application to intuitionistic bipolar neutrosophic graphs”, Annals of Communication in Mathematics, Vol 2, No. 2, pp. 121-140, 2019.
[32]Hussain, S. S., Hussain, R. J. and Smarandache, F., “Domination Number in Neutrosophic Soft Graphs”, Neutrosophic Sets and Systems, Vol 28, No. 1, pp. 228-244, 2019.
[33]Hussain, R. J., Hussain, S. S., Sahoo, S., Pal, M. and Pal, A., “Domination and Product Domination in Intuitionistic Fuzzy Soft Graphs”, International Journal of Advanced Intelligence Paradigms, 2020 (In Press), DOI:10.1504/IJAIP.2019.10022975.
[34]Smarandache, F., “A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic”, Rehoboth: American Research Press, 1999.
[35]Smarandache, F., “Neutrosophy, Neutrosophic Probability, Set, and Logic”, Amer../ Res. Press, Rehoboth, USA, 105 pages, 1998 http://fs.gallup.unm.edu/eBookneutrosophics4.pdf(4th edition).
[36]Smarandache, F., “Neutrosophic Graphs, in his book Symbolic Neutrosophic Theory”, Europa, Nova, 2015.
[37]Smarandache. F., “Neutro-Algebra is a Generalization of Partial Algebra”, International Journal of Neutrosophic Science (IJNS), Vol 2, No. 1, pp. 8-17, 2020.
[38]Smarandache, F., and Abobala, M, “n-Refined Neutrosophic Vector Spaces”, International Journal of Neutrosophic Science (IJNS), Vol 7, No. 1, pp. 47-54, 2020
[39]Smarandache, F., “Neutrosophic set, a generalisation of the intuitionistic fuzzy sets”, International Journal of Pure and Applied Mathematics, Vol 24, pp. 289-297, 2010.
[40]Wang, H., Smarandache, F., Zhang, Y. and Sunderraman, R., “Single-valued neutrosophic sets”, Multispace and Multistructure, Vol 4, pp. 410-413, 2010.
[41]Gau, W. L. and Buehrer, D. J.,“Vague sets”, IEEE Transactions on Systems. Man and Cybernetics, Vol 23, No. 2, pp. 610-614, 1993.
Cite This Article
Choose your preferred format