The Gutman Index and Schultz Index in the Random Phenylene Chains

Document Type : Research Paper

Authors

1 School of Mathematical Sciences‎, ‎Xinjiang Normal University, Urumqi‎, ‎Xinjiang 830054‎, ‎P‎. ‎R‎. ‎China‎

2 College of Mathematics and System Sciences‎, ‎Xinjiang University,‎ Urumqi‎, ‎Xinjiang 830046‎, ‎P. R. China

Abstract

The Gutman index and Schultz index are two topological indices‎. ‎In this paper‎, ‎we first give exact formulae for the expected values of the Gutman index and Schultz index of random phenylene chains‎, ‎and we will also get the average values of the Gutman index and Schultz index in phenylene chains.‎

Keywords

References

  1. M‎. ‎V‎. ‎Diudea‎, ‎I‎. ‎Gutman‎ and ‎L‎. ‎Jantschi‎, ‎Molecular Topology, Nova, Huntington, New York, 2001.
  2. H‎. ‎Wiener‎, ‎Structural determination of paraffin boiling points‎, ‎J. Amer. Chem. Soc. ‎69‎ (1947) ‎17-20.‎ ‎
  3. I‎. ‎Gutman‎, ‎Selected properties of the Schultz molecular topological index‎, ‎J. Chem. Info. Comput. Sci. 34‎ (1994) ‎1087-1089‎.  
  4. G‎. ‎Huang‎, ‎M‎. ‎Kuang‎ and ‎H‎. ‎Deng‎, ‎The expected values of Kirchhoff indices in the random polyphenyl and spiro chains‎, ‎Ars Math. Contemporanea ‎9‎ (‎2014) ‎197-207.
  5. X‎. ‎Y‎. ‎Geng‎, ‎P‎. ‎Wang‎, ‎L‎. ‎Lei‎ and ‎S‎. ‎J‎. ‎Wang‎, ‎On the Kirchhoff indices and the number of spanning trees of Möbius phenylenes chain and cylinder phenylenes chain‎, ‎Polycyclic Aromatic Compounds, DOI:10.1080/10406638.2019.1693405‎. ‎‎ ‎
  6. Q‎. ‎Xiao‎, ‎M‎. ‎Zeng‎, ‎Z‎. ‎Tang‎ and ‎H‎. ‎Deng‎, ‎The hexagonal chains with the first three maximal Mostar indices‎, ‎submitted‎. ‎‎‎
  7. Q‎. ‎Xiao‎, ‎M‎. ‎Zeng‎, ‎Z‎. ‎Tang‎ and ‎H‎. ‎Deng‎, ‎The hexagonal chains with the first three minimal Mostar indices‎, ‎submitted‎ ‎
  8. H‎. ‎Chen‎ and ‎F‎. ‎Zhang‎, ‎Resistance distance and the normalized Laplacian spectrum‎, ‎Discrete Appl. Math. 155  (2017) ‎654-661.‎ ‎
  9. I‎. ‎Gutman‎, ‎L‎. ‎Feng‎ and ‎G‎. ‎Yu‎, ‎Degree resistance distance of unicyclic graphs‎, ‎Trans. Combin. ‎1‎ (2012) ‎27-40.‎ ‎
  10. W‎. ‎Yang and ‎F‎. ‎Zhang‎, ‎Wiener index in random polyphenyl chains‎, ‎MATCH Commun. Math. Comput. Chem. ‎68‎ (2012) ‎371-376.‎ ‎
  11. W‎. ‎Wei‎ and ‎S‎. ‎Li‎, ‎Extremal phenylene chains with respect to the coefficients sum of the permanental polynomial‎, ‎the spectral radius‎, ‎the Hosoya index and the Merrifield Simmons index‎, ‎Discrete Appl. Math. 271 (2019) ‎205-217.‎ ‎
  12. Y‎. ‎Zuo‎, ‎Y‎. ‎Tang‎ and ‎H‎. ‎Deng‎, ‎The extremal graphs for (sum-) Balaban index of spiro and polyphenyl hexagonal chains, Iranian J. Math. Chem. ‎9‎ (2018) ‎241-254.‎ ‎
  13. L‎. ‎Zhang‎, ‎Q‎. ‎Li‎, ‎S‎. ‎Li and ‎M‎. ‎Zhang‎, ‎The expected values for the Schultz index‎, ‎Gutman index‎, ‎multiplicative degree-Kirchhoff index and additive degree-Kirchhoff index of a random polyphenylene chain‎, Discrete Appl. Math. 282 (2020) 243-256.
Iranian Journal of Mathematical Chemistry
Volume 12, Issue 2
June 2021
Pages 67-78

Files

Share

How to cite

Statistics