On the minimum semidefinite rank of signed graphs

被引：0
|
作者：
Matar, Nancy [1 ]
Mitchell, Lon H. [2 ]
Narayan, Sivaram K. [3 ]
机构：
[1] Western Carolina Univ, Dept Math & Comp Sci, Cullowhee, NC 28723 USA
[2] Univ S Florida, Dept Math & Stat, St Petersburg, FL 33701 USA
[3] Cent Michigan Univ, Dept Math, Mt Pleasant, MI 48859 USA
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2022年 / 642卷
关键词：
Minimum semidefinite rank; Signed graphs; Complete signed multigraphs;
D O I：
10.1016/j.laa.2022.02.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The (real) minimum semidefinite rank of a signed graph is the minimum rank among all real symmetric positive semidefinite matrices associated to the graph and having the given sign pattern. We give a new lower bound for the minimum semidefinite rank of a signed multigraph and show it equals a new upper bound for signed complete multigraphs. This allows a complete characterization of signed multigraphs with minimum semidefinite rank two. We also determine the minimum semidefinite rank of all signed wheel graphs. (C) 2022 Elsevier Inc. All rights reserved.
引用
收藏
页码：73 / 85
页数：13
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