Volume 3 , Issue 1 , PP: 19-26, 2022 | Cite this article as | XML | Html | PDF | Full Length Article
Surajit Kr. Nath 1 * , Bhimraj Basumatary 2 , E. Sampathkumar 3
Doi: https://doi.org/10.54216/JNFS.030102
In this paper, basic concepts of semigraph is introduced based on intuitionistic set. Definition of Intuitionistic Semigraph is introduced andUnion, intersection, and complement of intuitionistic semigraph is studied with graph.
Fuzzy set, Intuitionistic Set, Semigraph, Intuitionistic Semigraph
[1] Zadeh, L.A. “Fuzzy sets”. Inf. Control 1965, 8, 338–353.
[2] Sampathkumar, E. Deshpande C. M., Bam B. Y., Pushpalatha L. and Swaminathan V., “Semigraphs and their applications”, Academy of Discrete Mathematics and Applications India, (2019).
[3] Rosenfeld, A. “Fuzzy groups”. J. Math. Anal. Appl. 1971, 35, 512–517.
[4] Kauffman, A. “Introduction a la Theorie des Sous-EmsemblesFlous”. Masson et Cie: Paris, French, 1973.
[5] Zadeh, L.A. “Similarity relations and fuzzy orderings”. Inf. Sci. 1971, 3, 177–200.
[7] Bhattacharya, P. “Some remarks on fuzzy graphs”. Pattern Recognit. Lett. 1987, 6, 297–302
[8] Sunitha, M.S., Vijayakumar, A. “Complement of a fuzzy graph”. Indian J. Pure Appl. Math. 2002, 33, 1451–1464.
[9] Sunitha, M.S., Vijayakumar, A. A. “Characterization of fuzzy trees”. Inf. Sci. 1999, 113, 293–300.
[10] Mordeson, J.N., Nair, P.S. “Fuzzy Graphs and Fuzzy Hypergraphs”. Springer: Heidelberg, Germany, 2000; ISBN 978-3-7908-1854-3.
[11] Bhutani, K.R., Battou, A. “On M-strong fuzzy graphs”. Inf. Sci. 2003, 155, 103–109.
[12] Mathew, S., Sunitha, M.S. “Types of arcs in a fuzzy graph”. Inf. Sci. 2009, 179, 1760–1768.
[13] Mordeson, J.N., Chang-Shyh, P. “Operations on fuzzy graphs”. Inf. Sci. 1994, 79, 159–170.
[14] Nagoor Gani, A. Radha, K. “On regular fuzzy graphs”. J. Phys. Sci. 2008, 12, 33–44.
[15] Nagoor Gani, A., Radha, K. “Conjunction of two fuzzy graphs”. Int. Rev. Fuzzy Math. 2008, 3, 61–71.
[16] Nagoor Gani, A., Radha, K. “Some sequences in fuzzy graphs”. Far East J. Appl. Math. 2008, 31, 321–335.
[17] Nagoor Gani, A., Radha, K. “The degree of a vertex in some fuzzy graphs”. Int. J. Algorithms Comput. Math. 2009, 2, 107–116.
[18] Akram, M., Dudek, W.A. “Regular bipolar fuzzy graphs”. Neural Comput. Appl. 2012, 21, 197–205.
[19] Akram, M., Nawaz, S. “Operations on soft graphs”. Fuzzy Inf. Eng. 2015, 7, 423–449.
[20] Akram, M., Luqman, A. “Certain concepts of bipolar fuzzy directed hypergraphs”. Mathematics 2017, 5, 17.
[21] Sarwar, M., Akram, M.; Alshehri, N.O. “A new method to decision-making with fuzzy competition hypergraphs”. Symmetry 2018, 10, 404.
[22] Sampathkumar, E. “Generalized graph structures”. Bull. Kerala Math. Assoc. 2006, 3, 65–123.
[23] Dinesh, T. A Study on Graph Structures. “Incidence Algebras and Their Fuzzy Analogues”. Ph.D. Thesis, Kannur University, Kannur, India, 2011.
[24] Ramakrishnan, R.V.; Dinesh, T. “On generalised fuzzy graph structures”. Appl. Math. Sci. 2011, 5, 173–180.
[25] Atanassov, K. “Intuitionistic Fuzzy Sets: Theory and Applications”. Springer Physica-Verlag, Berlin, 1999.
[26] Karunambigai, M. G., Parvathi R., “Intuitionistic Fuzzy Graphs, Proceedings of 9th Fuzzy Days International Conference on Computational Intelligence, Advances in soft computing: Computational Intelligence,Theory and Applications, Springer-Verlag, Vol. 20, 2006, 139– 150.
[27] Bhutani, K. R., Rosenfeld A. “Strong arcs in fuzzy graphs”. Information Sciences, Vol.152, 2003, 319–322. 57.
[28] Coker D. “A note on intuitionistic sets and intuitionistic points”. Tr. J. of Mathematics 20 (1996) 343–351.
[29] Acharya B. D. and Sampathkumar E. “Graphoidal Covers and Graphoidal Covering Number of a Graph”. J. Pure ppl. Math., 18(10) (1987), 882–890.
[30] Armugam S., Acharya B. D. and Sampathkumar E. “Graphoidal Covers of a Graph: A Creative Review, Proc. National Workshop on Graph Theory and its Applications”. ManonmanianSundarnar University, Tirunelveli, 1–26 (1996), Tata-McGraw Hill, New Delhi, 1997.
