Open Access
Research Article
Laplacian energy of power fuzzy graphs with application in cryptography
S. Shiny Paulinpaulinshiny@gmail.comDepartment of Mathematics Loyola College University of MadrasChennai, Tamil Nadu, 600034, India0009-0006-1291-0484View full profile → , *T. BharathiCorresponding authordrtbharathi2024@gmail.comDepartment of Mathematics Loyola College University of MadrasChennai, Tamil Nadu, 600034, India0000-0003-2460-2682View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 08 Jan 2025
- Published Online:
- 01 Jan 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-2051
- Pages:
- 299–309
Abstract
The primary aim of this study is to present and expand on the idea of Laplacian energy within the context of power fuzzy graphs. The aim is to establish the Laplacian energy sequence for the power fuzzy graph with increasing power. The Laplacian spectrum and matrix are defined using the degree and adjacency matrices. The Laplacian energy of the power fuzzy graph is computed using eigenvalues of the corresponding Laplacian matrix and the size of the power fuzzy graph. The formal definition of the Laplacian matrix for power fuzzy graphs is defined, and the Laplacian energy sequence as power increases is computed. This concept is explored as a unique extension of fuzzy graphs and power graphs. Applying size, Laplacian matrix, and energy of regular power fuzzy graph theory to cryptography is a new method in this study.
Keywords
Subject Classifications
03B5205C7294D0594A60
References
[1] L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338-353 (Jun. 1965). https://doi.org/10.1016/s0019-9958(65)90241-xhttps://doi.org/10.1016/s0019-9958(65)90241-x.[2] A. Rosenfeld, “Fuzzy Graphs,” Fuzzy sets and their applications to cognitive and decision processes, In: Proceedings of the US-Japan Seminar on Fuzzy Sets and their Applications, pp. 77-95 (Jan. 1975).https://doi.org/10.1016/b978-0-12-775260-0.50008-6https://doi.org/10.1016/b978-0-12-775260-0.50008-6.[3] T. Bharathi, S. Shiny Paulin, and Bijan Davvaz, “A novel discussion on PFGs and their application in decision making,” Journal of applied mathematics & informatics, vol. 42, no. 1, pp. 123-137, 2024. https://doi.org/10.14317/jami.2024.123https://doi.org/10.14317/jami.2024.123.[4] R. Balakrishnan, “The energy of a graph,” Linear Algebra and its Applications, vol. 387, pp. 287-295 “Aug. 2004”. https://doi.org/10.1016/j.laa.2004.02.038https://doi.org/10.1016/j.laa.2004.02.038.[5] I. Gutman, “The Energy of a Graph: Old and New Results,” In: Betten, A., Kohnert, A., Laue, R., Wassermann, A. (eds) Algebraic Combinatorics and Applications, Springer, Berlin, Heidelberg, pp. 196-211 “Jan. 2001”. https://doi.org/10.1007/978-3-642-59448-9_13https://doi.org/10.1007/978-3-642-59448-9_13.[6] A. Narayanan and S. Mathew, “Energy of a fuzzy graph,” Annals of Fuzzy Mathematics and Informatics, vol. 6, no. 3, pp. 455-465 (2013).[7] Rahimi Sharbaf Sadegh and Fayazi Fatmeh, “Laplacian Energy of a Fuzzy Graph,” Iranian journal of mathemathical chemistry. Iranian journal of mathemathical chemistry, vol. 5, no. 1, pp. 1-10 (Mar. 2014) https://doi.org/10.22052/ijmc.2014.5214https://doi.org/10.22052/ijmc.2014.5214[8] S. Sharief Basha and E. Kartheek, “Laplacian Energy of an Intuitionistic Fuzzy Graph,” Indian Journal of Science and Technology, vol. 8, no. 33 (Dec. 2015). https://doi.org/10.17485/ijst/2015/v8i33/79899https://doi.org/10.17485/ijst/2015/v8i33/79899.[9] A. M. Philip, S. J. Kalayathankal, and J. V. Kureethara, “On the Laplacian energy of interval valued fuzzy graphs,” AIP conference proceedings, vol. 2261, no. 1, p. 030142 (Jan. 2020). https://doi.org/10.1063/5.0016779https://doi.org/10.1063/5.0016779.[10] Mahima Poonia and R. K. Bajaj, “On Laplacian energy of picture fuzzy graphs in site selection problem,” Journal of Intelligent & Fuzzy Systems, vol. 41, no. 1, pp. 481-498 (Jun. 2021). https://doi.org/10.3233/jifs-202131https://doi.org/10.3233/jifs-202131.[11] N. Rajagopal Reddy, M. Zubair Khan, S. Sharief Basha, A. Alahmadi, A. H. Alahmadi, and C. Lal Chowdhary, “The Laplacian Energy of Hesitancy Fuzzy Graphs in Decision-Making Problems,” Computer Systems Science and Engineering, vol. 44, no. 3, pp. 2637-2653 (2023). https://doi.org/10.32604/csse.2023.029255https://doi.org/10.32604/csse.2023.029255.[12] J. U. Rahman, U. Ali, and M. U. Rehman, “The Laplacian energy of diameter 4 trees,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 24, no. 1, pp. 119-128 (2021). https://doi.org/10.1080/09720529.2019.1670943 https://doi.org/10.1080/09720529.2019.167094.[13] R. Sarathy, and J. Ravi Sankar, “Laplacian energy and color based energy for graphs associated with commutative rings,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 27, no. 8, pp. 2431-2445 (2024). https://doi.org/10.47974/JDMSC-2016 https://doi.org/10.47974/JDMSC-2016.[14] T. Al-Hawary, S. Al-Shalaldeh, and M. Akram, “Certain Matrices and Energies of Fuzzy graphs,” TWMS Journal of Applied and Engineering Mathematics, vol. 2, no. 1 (Jan. 2023), https://doi.org/10.30546/2219-1259.14.1.2023.50https://doi.org/10.30546/2219-1259.14.1.2023.50.[15] T. Bharathi, S. Shiny Paulin, and S. Leo, “Cryptographic approach on edge regular PFG,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 28, no. 3, pp. 945-958 (2025). https://doi.org/10.47974/JDMSC-2216 https://doi.org/10.47974/JDMSC-2216.[16] T. Al-Hawary, “Complete fuzzy graphs,” International Journal of Mathematical Combinatorics, vol. 4, no. 4, pp. 26-34 (Jan. 2011). https://doi.org/10.5281/zenodo.825538https://doi.org/10.5281/zenodo.825538[17] N. Gani, and B. M. Ahamed, “Order and size in fuzzy Graph,” Bulletin of Pure and Applied Sciences, vol. 22, no. 1, pp. 145-148 (2003). https://doi.org/10.13140/2.1.3884.0969https://doi.org/10.13140/2.1.3884.0969.[18] T. Bharathi, S. Shiny Paulin, and M. Jeba Sherlin, “On regular PFG,” Journal of Applied Mathematics, Statistics and Informatics, vol. 20, no. 2, pp. 5-18 (Dec 2024). https://doi.org/10.2478/jamsi-2024-0005 https://doi.org/10.2478/jamsi-2024-0005.
Views: 122Downloads: 6Citations: 0
