极大次几何算术索引的极值树

IF 1 Q1 MATHEMATICS

Discrete Mathematics Letters Pub Date : 2022-01-27 DOI:10.47443/dml.2021.s207

A. Divya, A. Manimaran

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引用次数: 1

摘要

摘要对于图G，用GA（G）表示的G的几何算术指数被定义为所有边xy∈E（G）上的量2√dx×dy/（dx+dy）的和。这里，dx表示x的顶点度。对于n≥3阶的每棵树T，Vukičević和Furtula[J.Math.Chem.46（2009）1369–1376]证明了GA（T）≤4√2 3+（n−3）。这一结果在本文中得到了推广。特别地，对于n≥5阶且最大阶为∆的任意树T，证明了

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Extremal Trees for the Geometric-Arithmetic Index with the Maximum Degree

Abstract For a graph G, the geometric-arithmetic index of G, denoted by GA(G), is defined as the sum of the quantities 2 √ dx × dy/(dx + dy) over all edges xy ∈ E(G). Here, dx indicates the vertex degree of x. For every tree T of order n ≥ 3, Vukičević and Furtula [J. Math. Chem. 46 (2009) 1369–1376] demonstrated that GA(T ) ≤ 4 √ 2 3 + (n − 3). This result is extended in the present paper. Particularly, for any tree T of order n ≥ 5 and maximum degree ∆, it is proved that

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来源期刊

Discrete Mathematics Letters Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

12 weeks