Maximum energy bicyclic graphs containing two odd cycles with one common vertex

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2024-09-23 DOI:10.1016/j.dam.2024.09.014

Jing Gao, Xueliang Li, Ning Yang, Ruiling Zheng

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引用次数: 0

Abstract

The energy of a graph is the sum of the absolute values of all eigenvalues of its adjacency matrix. Let

P_{n}^{6, 6}

be the graph obtained from two copies of

C_{6}

joined by a path

P_{n - 10}

. In 2001, Gutman and Vidović (2001) conjectured that the bicyclic graph with the maximal energy is

P_{n}^{6, 6}

. This conjecture is true for bipartite bicyclic graphs. For non-bipartite bicyclic graphs, Ji and Li (2012) proved the conjecture for bicyclic graphs which have exactly two edge-disjoint cycles such that one of them is even and the other is odd. This paper is to prove the conjecture for bicyclic graphs containing two odd cycles with one common vertex.

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包含两个奇数循环和一个共同顶点的最大能量双环图

图形的能量是其邻接矩阵所有特征值的绝对值之和。假设 Pn6,6 是由 C6 的两个副本通过路径 Pn-10 连接而成的图。2001 年，Gutman 和 Vidović（2001 年）猜想能量最大的双环图是 Pn6,6。这一猜想适用于双方位双环图。对于非双方形双环图，Ji 和 Li（2012 年）证明了双环图的猜想，这些双环图恰好有两个边缘相交的循环，其中一个循环是偶数循环，另一个循环是奇数循环。本文将证明包含两个奇数循环且有一个共同顶点的双环图的猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.