L. E. Allem

collaborators

4 papers

math.CO2026

On the minimum number of eigenvalues of matrices associated with cographs

Luiz Emilio Allem, Martin FÃ¼rer, 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…

cs.SI2025

Multi-Community Spectral Clustering for Geometric Graphs

Luiz Emilio Allem, Konstantin Avrachenkov, Carlos Hoppen +2

In this paper, we consider the soft geometric block model (SGBM) with a fixed number $k \geq 2$ of homogeneous communities in the dense regime, and we introduce a spectral clusteri…

math.CO2025

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

Luiz Emilio Allem, Carlos Hoppen, JoÃ£o 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 $I^»$ ,…

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

Multi-Community Spectral Clustering for Geometric Graphs

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 $4$