The Least Eigenvalue of Unicyclic Graphs with Application to Spectral Spread

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2022-04-30 DOI:10.1142/s1005386722000219

Ji-Ming Guo, Gege Zhang, Zhiwen Wang, Pan-Pan Tong

引用次数: 0

Abstract

Let [Formula: see text] be the set of connected unicyclic graphs of order [Formula: see text] and girth [Formula: see text]. Let [Formula: see text] be obtained from a cycle [Formula: see text] (in an anticlockwise direction) by identifying [Formula: see text] with the root of a rooted tree [Formula: see text] of order [Formula: see text] for each [Formula: see text], where [Formula: see text] and [Formula: see text]. In this note, the graph with the minimal least eigenvalue (and the graph with maximal spread) in [Formula: see text] is determined.

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单环图的最小特征值及其在谱扩展中的应用

设[公式:见文]为有阶[公式:见文]和周长[公式:见文]的连通单环图的集合。通过将[公式:见文]与有根树[公式:见文]的顺序[公式:见文](公式:见文)(公式:见文)(公式:见文)(其中[公式:见文]和[公式:见文])的根(公式:见文)(逆时针方向)从一个循环[公式:见文]中得到[公式:见文]。在本文中，确定[公式:见文]中具有最小特征值的图(以及具有最大扩展的图)。

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

Algebra Colloquium 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

625

审稿时长

15.6 months

期刊介绍： Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.