Study of Bounds and Extremal Graphs of Symmetric Division Degree Index for Bicyclic Graphs with Perfect Matching

Document Type : Research Paper

Authors

Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh-221005, INDIA

Abstract

In this article, we complement the study of Pan and Li by computing the first five minimum values of the symmetric division degree (SDD) index attained by bicyclic graphs that have a perfect matching. One of our main contributions is identifying the graphs that attain the bounds. Further, we compute the upper bound of the SDD index for bicyclic graphs with a maximum degree of four, which admits a perfect matching and prove the bound is also tight by identifying the graphs that attain it.

Keywords

References

  1. Ali, S. Elumalai and T. Mansour, On the symmetric division deg index of molecular graphs, MATCH Commun. Math. Comput. Chem. 83 (2020) 205–220.
  2. Rajpoot and L. Selvaganesh, Bounds of the symmetric division deg index for trees and unicyclic graphs with a perfect matching, Iranian J. Math. Chem. 11 (3) (2020) 141–159.
  3. Rajpoot and L. Selvaganesh, Bounds and extremal graphs of the second reformulated Zagreb index for graphs with cyclomatic number at most three, Kuwait J. Sci. 49 (1) (2021) 1–21.
  4. Vasilyev, Upper and lower bounds of symmetric division deg index, Iranian J. Math. Chem. 5 (2) (2014) 91–98.
  5. Furtula, K. Ch. Das and I. Gutman, Comparative analysis of symmetric division deg index as a potentially useful molecular descriptor, Int. J. Quantum Chem. 118 (17) (2018) e25659.
  6. K. Gupta, V. Lokesha, S. B. Shetty and P. S. Ranjini, Graph operations on symmetric division deg index of graphs, Palestine J. Math. 6 (1) (2017) 280–286.
  7. K. Gupta, V. Lokesha, S. B. Shwetha and P. S. Ranjini, On the symmetric division deg index of a graph, Southeast Asian Bull. Math. 40 (1) (2016) 59–80.
  8. Liu, Y. Pan and J. Li, Tricyclic graphs with the minimum symmetric division deg index, Discrete Math. Lett. 3 (2020) 14–18.
  9. Vukičecić and M. Gašperov, Bond additive modeling 1. Adriatic indices, Croat. Chem. Acta. 83 (3) (2010) 243–260.
  10. A. Bondy, U. S. R. Murty, Graph Theory with Applications, Vol. 290, Macmillan London, Uk, 1976.
  11. L. Palacios, New upper bounds for the symmetric division deg index of graphs, Discrete Math. Lett. 2 (2019) 52–56.
  12. Romero-Valencia, J. C. Hernández-Gómez and G. Reyna-Hernández, On the inverse degree index and decomposition in graphs, Kuwait J. Sci. 46 (4) (2019) 14–22.
  13. Ch. Das, M. M. Matejić, E. I. Milovanović and I. Z. Milovanović, Bounds of symmetric division deg index of graphs, Filomat 33 (3) (2019) 683–698.
  14. Lokesha and T. Deepika, Symmetric division deg index of tricyclic and tetracyclic graphs, Int. J. Sci. Eng. Res. 7 (5) (2016) 53–55.
  15. Pan and J. Li, Graphs that minimizing symmetric division index deg, MATCH Commun. Math. Comput. Chem. 82 (1) (2019) 43–55.
  16. Shang, Estimating the distance Estrada index, Kuwait J. Sci. 43 (3) (2016) 14–19.
Iranian Journal of Mathematical Chemistry
Volume 13, Issue 2
June 2022
Pages 145-165

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