Some New Results on Mostar Index of Graphs

Document Type : Research Paper

Authors

1 Department of mathematics, Shahid Rajaee Teacher Training University

2 Department of Mathematics, SRTT University

3 Department of Mathematics, Srtt University

Abstract

A general bond additive index (GBA) can be defined as , where α(e) is edge contributions. The Mostar index is a new topological index whose edge contributions are α(e) = | nu - nv| in which nu is the number of vertices of lying closer to vertex u than to vertex v and nv can be defined similarly. In this paper, we propose some new results on the Mostar index based on the vertex-orbits under the action of automorphism group. In addition, we detrmined the structures of graphs with Mostar index equal 1. Finally, compute the Mostar index of a family of nanocone graphs.

Keywords

References

  1. J. Bok, B. Furtula, N. Jedlickova and R. Skrekovski, On extremal graphs of weighted Szeged index, MATCH Commun. Math. Comput. Chem. 82 (2019) 93−109.
  2.  J. Devillers and A. T. Balaban (Eds.), Topological Indices and Related Descriptors in QSAR and QSPR, Amsterdam, Netherlands, Gordon and Breach, 2000.
  3. M. V. Diudea and I. Gutman, Wiener-type topological indices, Croat. Chem. Acta 71 (1) (1998) 21−51.
  4. D. Djoković, Distance preserving subgraphs of hypercubes, J. Combin. Theory Ser. B 14 (1973) 263−267.
  5. A. A. Dobrynin, On the Wiener index of certain families of fibonacenes, MATCH Commun. Math. Comput. Chem. 70 (2013) 565−574.
  6. A. A. Dobrynin, The Szeged and Wiener indices of line graphs, MATCH Commun. Math. Comput. Chem. 79 (2018) 743−756
  7. A. A. Dobrynin and I. Gutman, On a graph invariant related to the sum of all distances in a graph, Publ. Inst. Math. Beograd. 56 (1994) 18−22.
  8. T. Došlić, I. Martinjak, R. Škrekovski, S. Tipurić Spužević and I. Zubac, Mostar index, J. Math. Chem. (2018), DOI:10.1007/s10910-018-0928-z.
  9. M. Ghorbani, X. Li, H. R. Maimani, Y. Mao, S. Rahmani and M. Rajabi-Parsa, Steiner (Revised) Szeged index of graphs, MATCH Commun. Math. Comput. Chem. 82 (2019) 733−742.
  10. M. Ghorbani; M. Songhori, Some topological indices of nanostar dendrimers, Iranian J. Math. Chem. 1 (2010) 57−65.
  11. M. Ghorbani and S. Rahmani, A note on Mostar index of a class of fullerenes, Int. J. of Chem. Model. 9 (2017) 245−256.
  12. I. Gutman, A formula for the Wiener number of trees and its extension to graphs containing cycles, Graph Theory Notes New York 27 (1994) 9−15.
  13. I. Gutman and A. A. Dobrynin, The Szeged index-a success story, Graph Theory Notes New York 34 (1998) 37−44.
  14. I. Gutman, P. V. Khadikar, P. V. Rajput and S. Karmarkar, The Szeged index of polyacenes, J. Serb. Chem. Soc. 60 (1995) 759−764.
  15. I. Gutman, S. Klavžar and B. Mohar (Eds), Fifty years of the Wiener index, MATCH Commun. Math. Comput. Chem. 35 (1997) 12−59.
  16. I. Gutman, Y. N. Yeh, S. L. Lee and Y. L. Luo, Some recent results in the theory of the Wiener number, Indian J. Chem. 32A (1993) 651−661.
  17. S. Klavžar and I. Gutman, A theorem on Wiener-type invariants for isometric subgraphs of hypercubes, Appl. Math. Lett. 19 (2006) 1129−1133.
  18. S. Klavžar, A. Rajapakse and I. Gutman, The Szeged and the Wiener index of graphs, Appl. Math. Lett. 9 (1996) 45−49.
  19. X. Li and M. Zhang, A note on the computation of revised (edge-)Szeged index in terms of canonical isometric embedding, MATCH Commun. Math. Comput. Chem. 81 (2019) 149−162.
  20. G. Rücker and C. Rücker, On topological indices, boiling points and cycloalkanes, J. Chem. Inf. Comput. Sci. 39 (1999) 788−802.
  21. B. E. Sagan, Y.-N. Yeh and P. Zhang, The Wiener polynomial of a graph, Int. J. Quantum. Chem. 60 (1996) 959−969.
  22. R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, Wiley−VCH, Weinheim, 2000.
  23. H. J. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947) 17−20.
Iranian Journal of Mathematical Chemistry
Volume 11, Issue 1
March 2020
Pages 33-42

Files

Share

How to cite

Statistics