论文标题
在图的算术几何指标上
On the arithmetic-geometric index of graphs
论文作者
论文摘要
最近，在数学化学中引入了第一个几何弧度指数$ ga $和算术几何指数$ ag $。在本文中，我们首先在$ ag $上获得一些下层和上限，并表征了极端图。我们还建立了$ ag $与其他拓扑指数之间的各种关系，例如第一个几何弧度指数$ ga $，atom-bond-bondeconnectivity Index $ abc $，对称的部门DEG INDEX $ SDD $，色数$ $χ$等等。最后，我们提供了一些足够的条件，用于$ ga（g）> ga（g-e）$或$ ag（g）> ag（g-e）$，用于图$ g $的边缘$ e $。特别是，对于第一个几何弧度指数，我们还提供了[3]中获得的Bollobás-erdős-type定理的细化。
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 $χ$ 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 Bollobás-Erdős-type theorem obtained in [3].
