L. Sibemberg

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20202026

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math.CO2026

On the minimum number of eigenvalues of matrices associated with cographs

Luiz Emilio Allem, Martin Fürer, Carlos Hoppen +2

A symmetric matrix $M = (m_{ij}) \in R^{n \times n}$ is said to be associated with an $n$ -vertex graph $G = (V, E)$ with vertex set ${v_{1}, \dots, v_{n}}$ if, for every $i \neq j…

math.CO2025

The minimum number of distinct eigenvalues of a threshold graph is at most $4$

Luiz Emilio Allem, Carlos Hoppen, João Lazzarin +2

In this note we show that the minimum number of distinct eigenvalues of a threshold graph is at most $4$ . Moreover, given any threshold graph $G$ and any nonzero real number $λ$ , w…

math.CO2025

On the minimum number of eigenvalues of trees of diameter seven

Luiz Emilio Allem, Carlos Hoppen, Lucas Siviero Sibemberg

The underlying graph $G$ of a symmetric matrix $M = (m_{ij}) \in R^{n \times n}$ is the graph with vertex set ${v_{1}, \dots, v_{n}}$ such that a pair ${v_{i}, v_{j}}$ with $i\neq j…

On the minimum number of eigenvalues of matrices associated with cographs

The minimum number of distinct eigenvalues of a threshold graph is at most 4

On the minimum number of eigenvalues of trees of diameter seven

The minimum number of distinct eigenvalues of a threshold graph is at most $4$