算术-几何指数和几何-算术指数之间的关系

Pub Date : 2024-04-01 DOI:10.59277/mrar.2024.26.76.1.17

K. Das, Tomas Vetrik, MO YONG-CHEOL

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引用次数: 0

摘要

图 G 的算术几何指数 AG(G) 和几何算术指数GA(G) 定义为 AG(G) = P uv∈E(G) dG(u)+dG(v)2√dG(u)dG(v)andGA(G) =Puv∈E(G)2√dG(u)dG(v)dG(u)+dG(v) 、其中，E(G) 是 G 的边集，dG(u) 和 dG(v) 分别是顶点 u 和 v 的度数。我们研究了给定大小、最小度和最大度的图 G 的 AG(G) 和 GA(G) 之间的关系。我们给出了 AG(G) + GA(G)、AG(G) - GA(G) 和 AG(G) - GA(G) 的下限和上限。所有边界都很尖锐。

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RELATIONS BETWEEN ARITHMETIC-GEOMETRIC INDEX AND GEOMETRIC-ARITHMETIC INDEX

The arithmetic-geometric index AG(G) and the geometric-arithmetic index GA(G) of a graph G are defined as AG(G) = P uv∈E(G) dG(u)+dG(v) 2 √ dG(u)dG(v) and GA(G) = P uv∈E(G) 2 √ dG(u)dG(v) dG(u)+dG(v) , where E(G) is the edge set of G, and dG(u) and dG(v) are the degrees of vertices u and v, respectively. We study relations between AG(G) and GA(G) for graphs G of given size, minimum degree and maximum degree. We present lower and upper bounds on AG(G) + GA(G), AG(G) − GA(G) and AG(G) · GA(G). All the bounds are sharp.

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