L. E. Allem

activity

20152026

most citedResolvent Energy of Unicyclic, Bicyclic and Tricyclic Graphs

8 citations · 10 across the 11 of their papers we have counts for

collaborators

Showing 2025Show all

3 papers · 1 filter

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, 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…

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 $4$