Super Neutrosophic $10^p$- Based Graceful Labeling Graphs and its Application
Govindan Vetrivel
1
(
)
Murugappan Mullai
2
(
)
Keywords: Graceful labeling, Intuitionistic fuzzy $10^p$ - based graceful labeling, Neutrosophic $10^p$- based graceful labeling, Super intuitionistic fuzzy $10^p$- based graceful labeling.,
Abstract :
Neutrosophic graph is used to deal with numerous real world problems and the attained solution is much more accurate than the previous fuzzy models. In this manuscript, a kind of graceful labeling based on $10^p$ is applied in intuitionistic and neutrosophic framework of graphs with super behaviour, that is quite useful to generalize the labeling structure. In addition, a methodology and an application for this labeling approach are discussed briefly.
[1] Zadeh LA. Fuzzy sets. Information and control. 1965; 8(3): 338-353. DOI: https://doi.org/10.1016/S0019-9958(65)90241-X
[2] Kaufmann A. Introduction to the theory of fuzzy subsets. New York: Academic Press Publishing; 1975.
[3] Rosenfeld A. Fuzzy graphs. In: Lotfi A. Zadeh, King-Sun Fu, Kokichi Tanaka, Masamichi Shimura. (eds.) Fuzzy Sets and their Applications to Cognitive and Decision Processes: Proceedings of the USJapan Seminar on Fuzzy Sets and their Applications, Held at the University of California, Berkeley, California, July 14, 1974. Amsterdam, The Netherlands: Elsevier; 1975. p.77-95. DOI: https://doi.org/10.1016/B978-0-12-775260-0.50008-6
[4] Bhattacharya P. Some remarks on fuzzy graphs. Pattern Recognition Letters. 1987; 6(5): 297-302. DOI: https://doi.org/10.1016/0167-8655(87)90012-2
[5] Bhuttani KR, Battou A. On M-strong fuzzy graphs. Information Sciences. 2003; (1-2): 103-109. DOI: https://doi.org/10.1016/S0020-0255(03)00157-9
[6] Nagoor Gani A, Rajalaxmi (a) Subahashini D. Properties of fuzzy labeling graph. Applied Mathematical Sciences. 2012; 6(70): 3461-3466.
https://m-hikari.com/ams/ams-2012/ams-69-72-2012/nagoorganiAMS69-72-2012-1.pdf
[7] Jahir Hussain R, Karthikkeyan RM. Fuzzy Graceful Graphs. Advances in Fuzzy Mathematics. 2017; 12(2): 309-317.
[8] Nagoor Gani A, Fathima Kani B, Afya Farhana MS. Fuzzy Edge Graceful Labeling On Wheel Graph, Fan Graph And Friendship Graph. American International Journal of Research in Science, Technology, Engineering & Mathematics, Special Issue of 5 th International Conference on Mathematical Methods and Computation (ICOMAC). 2019; 324-329.
[9] Jebesty Shajila R, Vimala S. Fuzzy vertex graceful labeling on wheel and fan graph. IOSR Journal of Mathematics. 2016; 12(2):45-49. DOI: http://doi.org/10.9790/5728-12214549
[10] Jebesty Shajila R, Vimala S. Graceful labeling for complete bipartite fuzzy graphs. British Journal of Mathematics & Computer Science. 2017; 22(2): 1-9. DOI: http://doi.org/10.9734/BJMCS/2017/32242
[11] Vimala S, Jebesty Shajila R. A note on fuzzy edge-vertex graceful labeling of Star graph and Helm graph. Advances in Theoretical and Applied Mathematics. 2016; 11(4): 331-338. DOI: https://doi.org/10.26483/ijarcs.v8i6.4327
[12] Solairaju A, Narppasalai Arasu T. Super fuzzy 10k -based graceful labeling of some classes of fuzzy trees related to path and star. Journal of Computer and Mathematical Sciences. 2018; 9(12): 2169-2177. DOI: https://doi.org/10.12988/pms.2020.91220
[13] Atanassov KT. Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 1986; 20(1): 87-96. DOI: https://doi.org/10.1016/S0165-0114(86)80034-3
[14] Parvathi R, Karunambigai MG. Intuitionistic Fuzzy Graphs. In: Reusch B. (eds.) Computational Intelligence, Theory and Applications. Berlin, Heidelberg: Springer; 2006.
[15] Akram M, Akmal R. Intuitionistic Fuzzy Graph Structures. Kragujevac Journal of Mathematics. 2017; 41(2): 219-237. DOI: http://doi.org/10.1016/j.fiae.2017.01.001
[16] Nagoor Gani A, Shajitha Begum S. Degree, order and size in intuitionistic fuzzy graphs. International Journal of Algorithms, Computing and Mathematics. 2010; 3(3): 11-16.
[17] Sahoo S, Pal M. Intuitionistic fuzzy labeling graphs. TWMS Journal of Applied and Engineering Mathematics. 2018; 8(2): 466-476.
[18] Rabeeh Ahamed T, Ismail Mohideen S, Prasanna A. Triangular intuitionistic fuzzy graceful labeling in some path related graphs. Advances and Applications in Mathematical Sciences. 2021; 20(6): 1077-1084.
[19] Devie Abirami P, Pradeep A, Akhilesh M, Santhosh Kumar S. Picture fuzzy graceful labeling for some graphs. Journal of Computational Analysis and Applications. 2024; 33(05): 541-548.
[20] Smarandache F. Neutrosophic set- a generalization of the intuitionistic fuzzy set. 2006 IEEE International Conference on Granular Computing, Atlanta, GA, USA: Springer; 2006, p. 38-42. DOI: http://doi.org/10.1109/GRC.2006.1635754.
[21] Smarandache F. A geometric interpretation of the neutrosophic set- A generalization of the intuitionistic fuzzy set. 2011 IEEE International Conference on Granular Computing, Kaohsiung, Taiwan: Springer; 2011, p. 602-606. DOI: http://doi.org/ 10.1109/GRC.2011.6122665
[22] Vasantha Kandasamy WB, Ilanthenral K, Smarandache F. (eds.) Neutrosophic graphs: A New Dimension to Graph Theory. Belgium: EuropaNova ASBL, Brussels; 2015.
[23] Broumi S, Smarandache F, Talea M, Bakali A. Single valued neutrosophic graphs: Degree, order and size. IEEE International Conference on Fuzzy Systems(FUZZ-IEEE), Vancouver, BC, Canada, 2444-2451, 2016. DOI: http://doi.org/10.1109/FUZZ-IEEE.2016.7738000
[24] Gomathi M, Keerthika V. Neutrosophic Labeling Graph. Neutrosophic Sets and Systems. 2019; 30(1): 261-272. DOI:
http://doi.org/ 10.5281/zenodo.3569706
[25] Ajay D, Chellamani P. Fuzzy magic labelling of neutrosophic path and star graph. Advances in Mathematics: Scientific Journal. 2020; 9(8): 6059-6070. DOI: http://doi.org/10.37418/amsj.9.8.74
[26] Sudha S, Lathamaheswari M, Broumi S, Smarandache F. Neutrosophic fuzzy magic labeling graph with its application in academic performance of the students. Neutrosophic Sets and Systems. 2023; 60: 88-112. DOI: http://doi.org/ 10.5281/zenodo.10224136
[27] Krishnaraj V, Vikramaprasad R. Some results on single valued neutrosophic bi-magic graphs. International Journal of Mechanical Engineering and Technology. 2018; 9(2):398-408.
[28] Logasoundarya ST, Vimala S. To analyse energy of the electric circuit by using neutrosophic labelling. Indian Journal of Science and Technology. 2024; 17(39):40304037. DOI: https://doi.org/10.17485/IJST/v17i39.2240
[29] Ajay D, Joseline Charisma J, Petaratip T, Hammachukiattikul P, Boonsatit N, Younis Jihad A, Rajchakit G. Pythagorean nanogeneralized closed sets with application in decision-making. Journal of Function Spaces. 2021; 2571301, 8 pages. DOI: https://doi.org/10.1155/2021/2571301
[30] Ajay D, Aldring J, Rajchakit G, Hammachukiattikul P, Boonsatit N. Sine trigonometry operational laws for complex neutrosophic sets and their aggregation operators in material selection. Computer Modeling in Engineering and Sciences. 2022; 130(2): 10331076. DOI: https://doi.org/10.32604/cmes.2022.018267
[31] Ajay D, Chellamani P. Pythagorean neutrosophic fuzzy graphs. International Journal of Neutrosophic Science. 2020; 11(2): 108-114. DOI: https://doi.org/10.54216/IJNS.0110205
[32] Ajay D, Karthiga S, Chellamani P. A study on labelling of pythagorean neutrosophic fuzzy graphs. Journal of Computational Mathematica. 2021; 5(1): 105-116. DOI: https://doi.org/10.26524/cm97
[33] Ajay D, Chellamani P, Rajchakit G, Boonsatit N, Hammachukiattikul P. Regularity of pythagorean neutrosophic graphs with an illustration in MCDM. AIMS Mathematics. 2022; 7(5): 94249442. DOI: https://doi.org/10.3934/math.2022523
[34] Vetrivel G, Mullai M, Rajchakit G. Product operations on pythagorean co-neutrosophic graphs and its application. Neutrosophic Sets and Systems. 2024; 72: 357-380. DOI: http://doi.org/10.5281/zenodo.13566972
[35] Li D-P, Cheng S-J, Cheng P-F, Wang J-Q, Zhang H-Y. A novel financial risk assessment model for companies based on heterogeneous information and aggregated historical data. PLoS ONE. 2018; 13(12): e0208166. DOI: https://doi.org/10.1371/journal.pone.0208166
[36] Shalihah M, Situmorang Tumpal P, Yusnita, Ridwan, Kalsum Ummy, Wahyudiyono. Implementation of financial risk management in improving the company’s financial stability. Maneggio. 2024; 1(6): 1-13. DOI: http://doi.org/10.62872/wcsn8237
