Extremal augmented Zagreb index of trees with given numbers of vertices and leaves

被引：9

作者：

Chen, Chaohui ^{[1
]}

Liu, Muhuo ^{[1
,2
]}

Gu, Xiaofeng ^{[3
]}

Das, Kinkar Chandra ^{[4
]}

机构：

[1] South China Agr Univ, Dept Math, Guangzhou 510642, Peoples R China

[2] South China Agr Univ, Res Ctr Green Dev Agr, Guangzhou 510642, Peoples R China

[3] Univ West Georgia, Dept Comp & Math, Carrollton, GA 30118 USA

[4] Sungkyunkwan Univ, Dept Math, Suwon 16419, South Korea

来源：

DISCRETE MATHEMATICS | 2022年 / 345卷 / 04期

基金：

新加坡国家研究基金会;

关键词：

Augmented Zagreb index; Atom-bond connectivity index; Topological index; Chemical graph theory; Extremal graphs; BOND CONNECTIVITY INDEX; ABC INDEX; GRAPHS;

D O I：

10.1016/j.disc.2021.112753

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The augmented Zagreb index AZ I(G) of a connected graph G is defined as AZ I(G) = Sigma(uv is an element of E(G))( d(u)d(v) / d(u) +d(v) - 2)(3) where d(u) and d(v) are the degrees of the end-vertices of an edge uv, respectively. We determine the unique tree with given numbers of vertices and leaves that minimizes augmented Zagreb index, and characterize the unique graph with minimum augmented Zagreb index in the class of connected graphs with given numbers of vertices and pendent vertices. Furthermore, we also determine the maximum augmented Zagreb index with the extremal trees characterized in the class of all trees with given numbers of vertices and leaves. (c) 2021 Elsevier B.V. All rights reserved.

引用

页数：15

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