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arXiv · 2010.03748

On the arithmetic-geometric index of graphs

Shu-Yu Cui·Weifan Wang·Gui-Xian Tian·Baoyindureng Wu
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Abstract

Very recently, the first geometric-arithmetic index $GA$ and arithmetic-geometric index $AG$ were introduced in mathematical chemistry. In the present paper, we first obtain some lower and upper bounds on $AG$ and characterize the extremal graphs. We also establish various relations between $AG$ and other topological indices, such as the first geometric-arithmetic index $GA$, atom-bond-connectivity index $ABC$, symmetric division deg index $SDD$, chromatic number $\chi$ and so on. Finally, we present some sufficient conditions of $GA(G)>GA(G-e)$ or $AG(G)>AG(G-e)$ for an edge $e$ of a graph $G$. In particular, for the first geometric-arithmetic index, we also give a refinement of Bollob\'{a}s-Erd\H{o}s-type theorem obtained in [3].

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Shu-Yu Cui, Weifan Wang, Gui-Xian Tian, Baoyindureng Wu. 2020-10-08. On the arithmetic-geometric index of graphs. https://arxiv.org/abs/2010.03748

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