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arXiv · 2308.12159

On bicyclic graphs with maximal Graovac-Ghorbani index

Rui Song·Saihua Liu·Jianping Ou
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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.

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Rui Song, Saihua Liu, Jianping Ou. 2023-08-23. On bicyclic graphs with maximal Graovac-Ghorbani index. https://arxiv.org/abs/2308.12159

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