On the minimum number of eigenvalues of matrices associated with cographs
Abstract
A symmetric matrix $M=(m_{ij}) \in \mathbb{R}^{n \times n}$ is said to be associated with an $n$-vertex graph $G=(V,E)$ with vertex set $\{v_1,\ldots,v_n\}$ if, for every $i \neq j$, we have $m_{ij} \neq 0$ if and only if $\{v_i,v_j\}\in E$. We prove that, for every cograph $G$, there is a matrix $M$ associated with $G$ for which the number of distinct eigenvalues is at most 4.
Fields of Study & Subjects
Graph theory and applications
Matrix Theory and Algorithms
Finite Group Theory Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 7 February 2026
- Language
- EN
- Document type
- Preprint