按直径的多重性列表：所有直径<7的树

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-06-03 DOI:10.1016/j.laa.2025.05.023

Charles R. Johnson , Benjamin Mudrak , Carlos M. Saiago

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引用次数: 0

摘要

本文从一个新的角度考虑图为给定树的厄米矩阵中所有多重表的确定问题。对于所有直径为<；7的树，展示了如何生成所有可能的列表。对于直径5和6，这包括许多非线性树。在此过程中，对于直径4（双星），给出了对每个实例的所有有序列表的第一个简洁而直接的描述。观察拓扑关系是有帮助的。

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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Multiplicity lists by diameter: All trees of diameter <7

This paper considers the problem of determining all multiplicity lists occurring among Hermitian matrices whose graph is a given tree from a new perspective. For all trees of diameter <7, it is shown how to generate all possible lists. For diameter 5 and 6, this includes many nonlinear trees. In the process, for diameter 4 (double stars), the first succinct and direct description of all ordered lists, for each instance, is given. Observations of topological relationships are helpful.

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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.