Constructing cospectral graphs via regular rational orthogonal matrix with level two and three

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-04-16 DOI:10.1016/j.disc.2025.114542

Lihuan Mao, Fu Yan

引用次数: 0

Abstract

Two graphs G and H are cospectral if their adjacency matrices share the same spectrum. Constructing cospectral non-isomorphic graphs has been studied extensively for many years and various constructions are known in the literature, e.g. the famous GM-switching method. In this paper, we shall construct cospectral graphs via regular rational orthogonal matrix Q with level two and three. We provide two straightforward algorithms to characterize the adjacency matrix A of the graph G such that

Q^{T} A Q

is again a (0,1)-matrix, and introduce two new switching methods to construct families of cospectral graphs which generalized the GM-switching to some extent.

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通过二级和三级规则有理正交矩阵构建余谱图

如果两个图G和H的邻接矩阵具有相同的谱，则它们是共谱。构造同谱非同构图已经被广泛研究了很多年，文献中有各种各样的构造方法，如著名的gm开关法。本文利用二阶和三阶正则有理正交矩阵Q构造同谱图。我们提供了两种简单的算法来表征图G的邻接矩阵A，使QTAQ再次成为(0,1)-矩阵，并引入了两种新的交换方法来构造共谱图族，在一定程度上推广了gm -交换。

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

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.