DOI QR코드

DOI QR Code

DOMINATING ENERGY AND DOMINATING LAPLACIAN ENERGY OF HESITANCY FUZZY GRAPH

  • K. SREENIVASULU (G.Pullaiah College of Engineering and Technology (Autonomous)) ;
  • M. JAHIR PASHA (Department of Computer Science and Engineering (Data Science), Rajeev Gandhi Memorial College of Engineering and Technology) ;
  • N. VASAVI (Department of Computer Science and Engineering (Artificial Intelligence), in Ashoka Womens Engineering College Kurnool) ;
  • RAJAGOPAL REDDY N (Department of Mathematical Sciences, Viswam Degree and P.G College) ;
  • S. SHARIEF BASHA (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology)
  • Received : 2021.08.02
  • Accepted : 2024.05.12
  • Published : 2024.07.30

Abstract

This article introduces the concepts of Energy and Laplacian Energy (LE) of Domination in Hesitancy fuzzy graph (DHFG). Also, the adjacency matrix of a DHFG is defined and proposed the definition of the energy of domination in hesitancy fuzzy graph, and Laplacian energy of domination in hesitancy fuzzy graph is given.

Keywords

References

  1. L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  2. A. Rosenfeld, Fuzzy Graphs, InFuzzy sets and their applications to cognitive and decision processes, Academic Press, New York, 1975, 75-95.
  3. R. Parvathi and M.G. Karunambigai, Intuitionistic Fuzzy Graphs, InComputational Intelligence, Theory and Applications: International Conference 9th Fuzzy Days in Dortmund, Germany, Sept. 18-20, 2006 Proceedings, Springer Berlin Heidelberg, 139-150.
  4. N. Anjali and S. Mathew, Energy of a fuzzy graph, Annals Fuzzy Math. Inf. 6 (2013), 455-465.
  5. R. Balakrishnan, The energy of a graph, Linear Algebra Appl. 387 (2004), 287-295. https://doi.org/10.1016/j.laa.2004.02.038
  6. Obbu Ramesh and S. Sharief Basha, An Intuitionistic Fuzzy Graph's Signless Laplacian Energy, International Journal of Engineering and Technology 7 (2018), 892-895.
  7. A. Somasundaram and S. Somasundaram, Domination in Fuzzy Graphs-I, Elsevier Science 19 (1998), 787-791. https://doi.org/10.1016/S0167-8655(98)00064-6
  8. Sadegh RahimiS harbaf, Fatmeh Fayazi, Laplacian Energy of a fuzzy Graph, Iranian Journal of Mathematical Chemistry 5 (2014), 31-40.
  9. R. Parvathi and G. Thamizhendhi, Domination in intuitionistic fuzzy graphs, Fourteenth Int. Conf. on IFSs, Sofia, 15-16, NIFS 16 (2010), 39-49.
  10. R. Parvathi and G. Thamizhendhi, Some results on domination number in products of intuitionistic fuzzy graphs, Annals of Fuzzy mathematics and Informatics 10 (2014), 1-20.
  11. E. Kartheek and S. Sharief Basha, The minimum dominating energy of a fuzzy graph, Journal of Information and Optimization Sciences 10 (2017), 443-53.
  12. R. Vijayaragavan, A. Kalimulla, and S. Sharief Basha, Dominating Laplacian Energy in Products of Intuitionistic Fuzzy Graphs, © Springer Nature Switzerland AG 2019 B. Rushi Kumar et al. (eds.), Applied Mathematics and Scientific Computing, Trends in Mathematics.
  13. R. Shakthivel, R. Vikramaprasad and N. Vinothkumar, Domination in Hesitancy Fuzzy Graphs, International Journal of Advanced Science and Technology 28 (2019), 1142-1156.
  14. S. Sharief Basha and E. Kartheek, Laplacian Energy of an Intuitionistic Fuzzy Graph, Indian Journal of Science and Technology 8 (2015), 1-7.
  15. V. Torra, Hesitant fuzzy sets, International Journal of Intelligent Systems 25 (2010), 529-39.
  16. Z. XU, Hesitant fuzzy sets and theory, Studies in Fuzziness and Soft Computing, Springer Verlag Publications, 2014.
  17. B. ZHU, Z. XU, and M. XIA, Dual hesitant fuzzy sets, Journal of Applied Mathematics, 1 (2012), 1-13. https://doi.org/10.5923/j.am.20110101.01
  18. T. Pathinathan, J.Jon Arockiaraj and J. Jesintha Rosline, Hesitancy Fuzzy Graphs, Indian Journal of Science and Technology 8 (2015), 1-5.
  19. C. Berge, Graphs and Hyper Graphs, North-Holland, Amsterdam, 309, 1973.
  20. O. Ore, Theory of graphs, Amer. Math. Soc. Colloq. Publi., Amer. Math. Soc, Providence, RI, 38, 1962.
  21. Rajagopal Reddy N and Sharief Basha S, The energy of hesitancy Fuzzy Graphs graphs, RRJ Eng. Technol. 12 (2023), 1-9.