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.
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}
}