构造具有不可约特征多项式的共谱图

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-05-06 DOI:10.1016/j.laa.2025.04.019

Qian Yu, Yuchao Li, Fenjin Liu

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引用次数: 0

摘要

图的特征多项式定义为其邻接矩阵的特征多项式，其根为图的特征值。图特征值的多集称为邻接谱。如果两个图具有相同的邻接谱，则它们是共谱。研究了有理数域上具有不可约特征多项式的同谱图。给出了无穷多对具有不可约特征多项式的有根共谱图、广义共谱图和共谱电晕图。

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Constructing cospectral graphs with irreducible characteristic polynomials

Graph characteristic polynomial is defined as that of its adjacency matrix, whose roots are the eigenvalues of the graph. The multi-set of graph eigenvalues is called the adjacency spectrum. Two graphs are cospectral if they have the same adjacency spectrum. We study the cospectral graphs with irreducible characteristic polynomials over rational number field. And we give infinitely many pairs of rooted cospectral graphs, generalized cospectral graphs and cospectral corona graphs with irreducible characteristic polynomials.

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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.