The automorphism group and plain eigenvalues of a graph

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-05-19 DOI:10.1016/j.laa.2025.05.011

Wei Wang, Xinyue Wang

引用次数: 0

Abstract

We introduce the plain polynomial associated with a graph G, which is defined to be the quotient of the characteristic polynomial and the main polynomial of G. For a graph G with a square-free plain polynomial, we establish an upper bound on the order of its automorphism group in terms of the number of irreducible factors of the plain polynomial over

Q

. This improves the previous upper bound using the characteristic polynomial (G. Criscuolo, C.-M. Kwok, A. Mowshowitz, and R. Tortora, The group and the minimal polynomial of a graph, J. Combin. Theory Ser. B 29 (1980) 293–302).

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图的自同构群和平面特征值

我们引入了与图G相关的平面多项式，它被定义为特征多项式与G的主多项式之商。对于具有无平方平面多项式的图G，我们根据其q上的平面多项式的不可约因子的个数建立了其自同构群的阶上界，改进了先前使用特征多项式的上界。郭，a . Mowshowitz和R. Tortora，图的群和最小多项式，J. Combin。Ser的理论。B 29(1980) 293-302)。

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

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.