Sharp bounds for the general Randic index of graphs with fixed number of vertices and cyclomatic number

被引：0

作者：

Su, Guifu ^{[1
]}

Wu, Yue ^{[1
]}

Qin, Xiaowen ^{[1
]}

Du, Junfeng ^{[1
]}

Guo, Weili ^{[1
]}

Zhang, Zhenghang ^{[1
]}

Song, Lifei ^{[1
]}

机构：

[1] Beijing Univ Chem Technol, Coll Math & Phys, Beijing 100029, Peoples R China

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 12期

关键词：

extremal graphs; the general Randic index; cyclomatic number; sharp bounds; 2ND ZAGREB INDEX; UNICYCLIC GRAPHS; ALPHA;

D O I：

10.3934/math.20231502

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The cyclomatic number, denoted by gamma, of a graph G is the minimum number of edges of G whose removal makes G acyclic. Let G(n)(gamma) be the class of all connected graphs with order n and cyclomatic number gamma. In this paper, we characterized the graphs in G(n)(gamma) with minimum general Randic index for gamma >= 3 and 1 <= alpha <= 39 /25. These extend the main result proved by A. Ali, K. C. Das and S. Akhter in 2022. The elements of G(n)(gamma) with maximum general Randic index were also completely determined for gamma >= 3 and alpha >= 1.

引用

页码：29352 / 29367

页数：16

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