Minimum semidefinite rank of signed graphs and partial 3-trees

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-02-13 DOI:10.1016/j.laa.2025.02.018

Ansam I. Al-Aqtash , Lon H. Mitchell , Sivaram K. Narayan

引用次数: 0

Abstract

In this paper, the sign patterns of real symmetric positive semidefinite matrices are used to study the real minimum semidefinite rank of signed graphs. The signed graphs whose real minimum semidefinite rank is one are characterized. It is shown that the real minimum semidefinite rank of a signed graph is at most the order of the graph minus two if and only if the signed graph contains a positive cycle. By considering orthogonal vertex removal in signed graphs it is shown that the real minimum semidefinite rank of a partial 3-tree is equal to its associated reduction number.

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有符号图和偏3树的最小半定秩

本文利用实对称正半定矩阵的符号模式研究了符号图的实最小半定秩问题。对实最小半定秩为1的符号图进行了刻画。证明了当且仅当有符号图包含正循环时，有符号图的实最小半定秩不大于图的阶- 2。通过考虑符号图的正交顶点去除，证明了偏3树的实最小半定秩等于它的相关约简数。

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.