Characterization of Graphs with Some Normalized Laplacian Eigenvalue Having Multiplicity $$n{-}4$$

IF 1.1 4区数学 Q1 MATHEMATICS

Communications in Mathematics and Statistics Pub Date : 2024-07-23 DOI:10.1007/s40304-024-00395-5

Shaowei Sun

引用次数: 0

Abstract

The spectrum of the normalized Laplacian matrix of a graph provides a lot of structural information of the graph, and it has applications in numerous areas and in different guises. In this paper, we completely characterize all connected graphs of order $n\ge 25$ with some normalized Laplacian eigenvalue $\rho \in \big (0,\,\frac{n-1}{n-2}\big )$ having multiplicity $n{-4}$.

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具有某些乘数为 $$n{-}4$$ 的归一化拉普拉奇特征值的图形特征

一个图的归一化拉普拉奇矩阵的频谱提供了该图的大量结构信息，它以不同的面貌应用于众多领域。在本文中，我们完整地描述了所有阶为（n\ge 25\ ）的连通图，这些图具有某个归一化拉普拉斯特征值（\rho \in \big (0,\,\frac{n-1}{n-2}\big )\），其乘数为（n{-4}\）。

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

Communications in Mathematics and Statistics Mathematics-Statistics and Probability

CiteScore

1.80

自引率

0.00%

发文量

期刊介绍： Communications in Mathematics and Statistics is an international journal published by Springer-Verlag in collaboration with the School of Mathematical Sciences, University of Science and Technology of China (USTC). The journal will be committed to publish high level original peer reviewed research papers in various areas of mathematical sciences, including pure mathematics, applied mathematics, computational mathematics, and probability and statistics. Typically one volume is published each year, and each volume consists of four issues.