The second geometric-arithmetic index for trees and unicyclic graphs

IF 1 Q4 CHEMISTRY, MULTIDISCIPLINARY Iranian journal of mathematical chemistry Pub Date : 2018-12-01 DOI:10.22052/IJMC.2017.81079.1277
N. Dehgardi, H. Aram, A. Khodkar
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引用次数: 0

Abstract

Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$, where $n_u$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms of the order and maximum degree of the tree. We also find a sharp upper bound for $GA_2(G)$, where $G$ is a unicyclic graph, in terms of the order, maximum degree and girth of $G$. In addition, we characterize the trees and unicyclic graphs which achieve the upper bounds.
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树和单环图的第二几何算术索引
设$G$是一个有边集$E(G)$的有限简单图。第二个几何算术索引定义为$GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$,其中$n_u$表示$G$中靠近$u$而不是靠近$v$的顶点数。本文给出了$GA_2(T)$,其中$T$为树,关于树的阶数和最大度的一个明显的上界。我们还发现了$GA_2(G)$,其中$G$是单环图,关于$G$的阶数、最大度和周长,有一个明显的上界。此外,我们还刻画了达到上界的树和单环图。
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来源期刊
Iranian journal of mathematical chemistry
Iranian journal of mathematical chemistry CHEMISTRY, MULTIDISCIPLINARY-
CiteScore
2.10
自引率
7.70%
发文量
0
期刊最新文献
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