Unicyclic graphs with large energy

被引：15

作者：

Andriantiana, Eric Ould Dadah ^{[1
]}

Wagner, Stephan ^{[1
]}

机构：

[1] Univ Stellenbosch, Div Math, Dept Math Sci, ZA-7602 Matieland, South Africa

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2011年 / 435卷 / 06期

基金：

新加坡国家研究基金会;

关键词：

Maximum energy; Unicyclic graphs; Coulson formula; MINIMAL ENERGY; MOLECULAR GRAPHS; MAXIMAL ENERGY; HOSOYA INDEX; TREES;

D O I：

10.1016/j.laa.2011.03.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the energy (i.e., the sum of the absolute values of all eigenvalues) of so-called tadpole graphs, which are obtained by joining a vertex of a cycle to one of the ends of a path. By means of the Coulson integral formula and careful estimation of the resulting integrals, we prove two conjectures on the largest and second-largest energy of a unicyclic graph due to Caporossi, Cvetkovic, Gutman and Hansen and Gutman, Furtula and Hua, respectively. Moreover, we characterise the non-bipartite unicyclic graphs whose energy is largest. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：1399 / 1414

页数：16

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