A Study on Degree Based Topological Indices of Harary Subdivision Graphs With Application

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-63
Published: Apr 8, 2024
Cite as:
Mukhtar Ahmad, Ather Qayyum, Gulnaz Atta, Siti Suzlin Supadi, Muhammad Saleem, Usman Ali, A Study on Degree Based Topological Indices of Harary Subdivision Graphs With Application, Int. J. Anal. Appl., 22 (2024), 63.

Main Article Content

Mukhtar Ahmad, Ather Qayyum, Gulnaz Atta, Siti Suzlin Supadi, Muhammad Saleem, Usman Ali

Abstract

Combinatorial design theory and graph decompositions play a critical role in the exploration of combinatorial design theory and are essential in mathematical sciences. The process of graph decomposition involves partitioning the set of edges in a graph G. An n-sun graph, characterized by a cycle with an edge connecting each vertex to a terminating vertex of degree one, is introduced in this study. The concept of n-sun decomposition is applied to certain even-order graphs. The indices covered in this study include the general connectivity index of the harary graphs, Zagreb indices, symmetric division degree indices and randic indices.

Article Details

References

  1. W.D. Wallis, Magic Graphs, Birkhäuser, Basel, (2001).
  2. B. Alspach, J.C. Bermond, D. Sotteau, Decomposition Into Cycles I: Hamilton Decompositions, in: G. Hahn, G. Sabidussi, R.E. Woodrow (Eds.), Cycles and Rays, Springer Netherlands, Dordrecht, 1990: pp. 9–18. https://doi.org/10.1007/978-94-009-0517-7_2.
  3. B. Alspach, The Wonderful Walecki Construction, Bull. Inst. Comb. Appl. 52 (2008), 7–20.
  4. B. Alspach, H. Gavlas, Cycle Decompositions of Kn and Kn − I, J. Comb. Theory, Ser. B. 81 (2001), 77–99. https://doi.org/10.1006/jctb.2000.1996.
  5. D.B. West, Introduction to Graph Theory, Prentice Hall, Upper Saddle River, (2001).
  6. J.L. Gross, J. Yellen, Handbook of Graph Theory, CRC Press, Boca Raton, (2004).
  7. M.H. Khalifeh, H. Yousefi-Azari, A.R. Ashrafi, The First and Second Zagreb Indices of Some Graph Operations, Discr. Appl. Math. 157 (2009), 804–811. https://doi.org/10.1016/j.dam.2008.06.015.
  8. G.H. Shirdel, H. Rezapour, A.M. Sayadi, The Hyper-Zagreb Index of Graph Operations, 4 (2013), 213–220.
  9. S.M. Sankarraman, A Computational Approach on Acetaminophen Drug Using Degree-Based Topological Indices and M-Polynomials, Biointerface Res. Appl. Chem. 12 (2021), 7249–7266. https://doi.org/10.33263/briac126.72497266.
  10. I. Gutman, Multiplicative Zagreb Indices of Trees, Bull. Soc. Math. Banja Luka. 18 (2011), 17–23.
  11. S. Hayat, M. Imran, On Degree Based Topological Indices of Certain Nanotubes, J. Comput. Theor. Nanosci. 12 (2015), 1599–1605. https://doi.org/10.1166/jctn.2015.3935.
  12. E. Estrada, L. Torres, L. Rodriguez, I. Gutman, An Atom-Bond Connectivity Index: Modelling the Enthalpy of Formation of Alkanes, Indian. J. Chem. 37A (1998), 849–855.
  13. X. Ren, X. Hu, B. Zhao, Proving a Conjecture Concerning Trees With Maximal Reduced Reciprocal Randic Index, MATCH Commun. Math. Comput. Chem. 76 (2016), 171–184.
  14. B. Furtula, I. Gutman, A Forgotten Topological Index, J. Math. Chem. 53 (2015), 1184–1190. https://doi.org/10.1007/s10910-015-0480-z.
  15. A.R. Ashrafi, M. Mirzargar, PI, Szeged and Edge Szeged of an Infinite Family of Nanostardendrimers, Indian J. Chem. 47A (2008), 538–541.
  16. Z. Chen, M. Dehmer, F. Emmert-Streib, Y. Shi, Entropy Bounds for Dendrimers, Appl. Math. Comput. 242 (2014), 462–472. https://doi.org/10.1016/j.amc.2014.05.105.
  17. M.V. Diudea, A.E. Vizitiu, M. Mirzagar, A.R. Ashrafi, Sadhana Polynomial in Nano-Dendrimers, Carpathian J. Math. 26 (2010), 59–66.
  18. Z. Hassan Niazi, M.A.T. Bhatti, M. Aslam, Y. Qayyum, M. Ibrahim, A. Qayyum, d-Lucky Labeling of Some Special Graphs, Amer. J. Math. Anal. 10 (2022), 3–11. https://doi.org/10.12691/ajma-10-1-2.
  19. A. Asghar, A. Qayyum, N. Muhammad, Different Types of Topological Structures by Graphs, Eur. J. Math. Anal. 3 (2022), 3.
  20. M. Ahmad, S. Hussain, U. Parveen, I. Zahid, M. Sultan, A. Qayyum, On Degree-Based Topological Indices of Petersen Subdivision Graph, Eur. J. Math. Anal. 3 (2023), 20.
  21. M. Ahmad, M.J. Hussain, G. Atta, S. Raza, I. Waheed, A. Qayyum, Topological Evaluation of Four Para-Line Graphs Absolute Pentacene Graphs Using Topological Indices, Int. J. Anal. Appl. 21 (2023), 66. https://doi.org/10.28924/2291-8639-21-2023-66.
  22. R.M.K. Iqbal, M. Ahmad, A. Qayyum, S.S. Supadi, M.J. Hussain, S. Raza, On Degree-Based Topological Indices of Toeplitz Graphs, Int. J. Anal. Appl. 21 (2023), 111. https://doi.org/10.28924/2291-8639-21-2023-111.