Minimum semidefinite rank of signed graphs and partial 3-trees

Authors

• Ansam I. Al-Aqtash, Marshall University
• Lon H. Mitchell, Eastern Michigan University
• Sivaram K. Narayan, Central Michigan University

Document Type

Article

Publication Date

2025

Department/School

Mathematics

Publication Title

Linear Algebra and Its Applications

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.

Comments

L. H. Mitchell is a faculty member in EMU's Department of Mathematics and Statistics.

Link to Published Version

DOI: 10.1016/j.laa.2025.02.018

Recommended Citation

Al-Aqtash, A. I., Mitchell, L. H., & Narayan, S. K. (2025). Minimum semidefinite rank of signed graphs and partial 3-trees. Linear Algebra and Its Applications, 711, 126–142. https://doi.org/10.1016/j.laa.2025.02.018