The randic index in neutrosophic graphs and its applications

Authors

  • Suriyakumar G * Department of Mathematics, Islamiah College (Autonomous), Vaniyambadi, Affiliated to Thiruvalluvar University, Vellore, Tamil Nadu, India. https://orcid.org/0009-0007-0061-5696
  • V. J. Sudhakar Department of Mathematics, Islamiah College (Autonomous), Vaniyambadi, Affiliated to Thiruvalluvar University, Vellore, Tamil Nadu, India.

https://doi.org/10.48313/uda.vi.71

Abstract

 In this paper introduces and investigates the Randic index for unclear graphs and neutrosophic subgraphs. It effective models in uncertainty and imprecision in edge and vertex relations. This study examines the Randic index’s features for neutrosophic graphs and the impact of isomorphism between graphs. Furthermore, the notion is extended to directed neutrosophic graphs, offering a novel approach to analysing directed structures under uncertainty. The Randic index can help determine the best site for a waste management plant, as demonstrated in a real-world example. This approach emphasises the Randic index’s practical importance in urban planning and infrastructure development, demonstrating its larger impact across several disciplines. 

Keywords:

Randic index, Neutrosophic graph, Randic index in neutrosophic graph

References

  1. [1] Ali, M., & Smarandache, F. (2017). Complex neutrosophic set. Neural computing and applications, 28(7), 1817-1834. https://doi.org/10.1007/s00521-015-2154-y
  2. [2] Dey, A., Kumar, R., Broumi, S., & Bhowmik, P. (2022). Different types of operations on neutrosophic graphs. International journal of neutrosophic science, 19(2), 87-94. https://doi.org/10.54216/IJNS.190208
  3. [3] Borzooei, R. A., & Rashmanlou, H. (2015). Degree of vertices in vague graphs. Journal of applied mathematics & informatics, 33(5_6), 545-557. http://dx.doi.org/10.14317/jami.2015.545
  4. [4] Borzooei, R. A., Rashmanlou, H., Samanta, S., & Pal, M. (2016). Regularity of vague graphs. Journal of intelligent & fuzzy systems, 30(6), 3681-3689. https://doi.org/10.3233/IFS-162114
  5. [5] Kakkad, K. K., & Sharma, S. (2017). New approach on regular fuzzy graph. Global journal of pure and applied mathematics, 13(7), 3753-3766. https://www.ripublication.com/gjpam17/gjpamv13n7_71.pdf
  6. [6] Mohanta, K., Dey, A., & Pal, A. (2021). A note on different types of product of neutrosophic graphs. Complex & intelligent systems, 7(2), 857-871. https://doi.org/10.1007/s40747-020-00238-0
  7. [7] Huang, L., Hu, Y., Li, Y., Kumar, P. K., Koley, D., & Dey, A. (2019). A study of regular and irregular neutrosophic graphs with real life applications. Mathematics, 7(6), 551. https://doi.org/10.3390/math7060551
  8. [8] Gani, A. N., & Ahamed, M. B. (2003). Order and size in fuzzy graphs. Bulletin of pure and applied sciences, 22(1), 145-148. https://doi.org/10.13140/2.1.3884.0969
  9. [9] Gani, A. N., & Radha, K. (2008). On regular fuzzy graphs. Journal of physical sciences, 12, 33–40. http://vu.dspaces.org/handle/123456789/755
  10. [10] Gani, A. N., & Latha, S. R. (2012). On irregular fuzzy graphs. Applied mathematical sciences, 6(11), 517-523. https://m-hikari.com/ams/ams-2012/ams-9-12-2012/nagoorganiAMS9-12-2012-1.pdf
  11. [11] Yaqoob, N., & Akram, M. (2018). Complex neutrosophic graphs. Infinite study. https://fs.unm.edu/neut/ComplexNeutrosophicGrap.pdf
  12. [12] Nguyen, H. T., Kandel, A., & Kreinovich, V. (2000, May). Complex fuzzy sets: Towards new foundations. In Ninth IEEE international conference on fuzzy systems. FUZZ-IEEE 2000 (cat. No. 00CH37063) (Vol. 2, pp. 1045-1048). IEEE. https://doi.org/10.1109/FUZZY.2000.839195
  13. [13] Broumi, S., Talea, M., Bakali, A., & Smarandache, F. (2016). Single valued neutrosophic graphs. Journal of new theory, (10), 86-101. https://dergipark.org.tr/en/pub/jnt/article/381241
  14. [14] Shah, N., & Broumi, S. (2016). Irregular neutrosophic graphs. Neutrosophic sets and systems, 13(1), 6. https://digitalrepository.unm.edu/cgi/viewcontent.cgi?article=1154&context=nss_journal
  15. [15] Hussain, S. S., Hussain, R. J., & Smarandache, F. (2019). On neutrosophic vague graphs. Neutrosophic sets and systems, 28, 69–86. https://fs.unm.edu/NSS/OnNeutrosophicVagueGraphs.pdf
  16. [16] Sudhakar, V. J., Mohamed Ali, A., & Vinoth, D. (2016). Interval valued signed neutrosophic graph. International journal of mathematical archive, 9(9), 35–43. https://fs.unm.edu/neut/IntervalValuedSignedNeutrosophic.pdf
  17. [17] Sudhakar, V. J., Ali, A. M., Vinoth, D., & Sathishkumar, G. (2016). Self-centered interval valued neutrosophic graph. Neutrosophic sets and systems, 11, 44–50. https://fs.unm.edu/neut/SelfCenteredIntervalValued.pdf
  18. [18] Sudhakar, V. J., & Jayaprakasam, S. (2019). Interval valued signed neutrosophic graph. International journal of mathematical archive, 9(9), 35–43. https://fs.unm.edu/neut/IntervalValuedRegularNeutrosophic.pdf
  19. [19] Sudhakar, V. J., Navaneethakumar, V., & Yuvaraj, V. (2019). Self-centered interval valued neutrosophic graphs. International journal of science and humanities, 5(2), 86–102. https://fs.unm.edu/neut/SelfCenteredIntervalValued.pdf
  20. [20] Jagadeeswari, L., & Sudhakar, V. J. (2021). Bipolar interval valued signed neutrosophic graphs. Malaya journal of matematik, 9(1), 1086-1094. https://www.malayajournal.org/articles/MJM09010189.pdf
  21. [21] Sudhakar, V., Hussainy, S. T., & Donganont, M. (2025). Complex neutrosophic vague soft graphs. Neutrosophic sets & systems, 87. https://fs.unm.edu/NSS/49VagueSoft.pdf
  22. [22] Fallah Andevari, A., & Talebi, Y. (2024). Novel concepts of the Randic index in vague graphs with applications. International journal of nonlinear analysis and applications, 15(11), 271-283. https://doi.org/10.22075/ijnaa.2023.30895.4513
  23. [23] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X

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Published

2026-03-22

Issue

Vol. 3 No. 1 (2026): Uncertainty Discourse and Applications

Section

Articles

How to Cite

G, S., & Sudhakar, V. J. (2026). The randic index in neutrosophic graphs and its applications. Uncertainty Discourse and Applications, 3(1), 72-88. https://doi.org/10.48313/uda.vi.71

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