复单位增益图的对称性及其谱

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-05-20 DOI:10.1016/j.laa.2025.05.012

Pepijn Wissing, Edwin R. van Dam

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引用次数: 0

摘要

复杂的单位增益图可能表现出各种各样的对称性。在这项工作中，我们探讨了结构对称、谱对称和符号对称在这样的图中，以及它们各自的相互关系。我们的主要结果是一个结构，将任意复杂的单位增益图转换成无限多个切换不同的图，其谱对称并不意味着符号对称。这为最近在有符号图的背景下处理的存在性问题的类比提供了一个更一般的答案。

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Symmetry in complex unit gain graphs and their spectra

Complex unit gain graphs may exhibit various kinds of symmetry. In this work, we explore structural symmetry, spectral symmetry and sign-symmetry in such graphs, and their respective relations to one-another. Our main result is a construction that transforms an arbitrary complex unit gain graph into infinitely many switching-distinct ones whose spectral symmetry does not imply sign-symmetry. This provides a more general answer to the analogue of an existence question that was recently treated in the context of signed graphs.

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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.