Subdivision and graph eigenvalues

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-02-04 DOI:10.1016/j.laa.2025.01.044

Hitesh Kumar, Bojan Mohar , Shivaramakrishna Pragada, Hanmeng Zhan

引用次数: 0

Abstract

This paper investigates the asymptotic nature of graph spectra when some edges of a graph are subdivided sufficiently many times. In the special case where all edges of a graph are subdivided, we find the exact limits of the k-th largest and k-th smallest eigenvalues for any fixed k. Given a graph, we show that after subdividing sufficiently many times, all but

O (1)

eigenvalues of the new graph will lie in the interval

[- 2, 2]

. We examine the eigenvalues of the new graph outside this interval, and we prove several results that might be of independent interest.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.