English

On bicyclic graphs with maximal Graovac-Ghorbani index

Combinatorics 2023-08-24 v1

Abstract

Graovac-Ghorbani index is a new version of the atom-bond connectivity index. D. Pacheco et al. [D. Pacheco, L. de Lima, C. S. Oliveira, On the Graovac-Ghorbani Index for Bicyclic Graph with No Pendent Vertices, MATCH Commun. Math. Comput. Chem. 86 (2021) 429-448] conjectured a sharp lower and upper bounds to the Graovac-Ghorbani index for all bicyclic graphs. Motivated by their nice work, in this paper we determine the maximal Graovac-Ghorbani index of bicyclic graphs and characterize the corresponding extremal graphs, which solves one of their Conjectures.

Keywords

Cite

@article{arxiv.2308.12159,
  title  = {On bicyclic graphs with maximal Graovac-Ghorbani index},
  author = {Rui Song and Saihua Liu and Jianping Ou},
  journal= {arXiv preprint arXiv:2308.12159},
  year   = {2023}
}
R2 v1 2026-06-28T12:02:32.827Z