8 citations · 10 across the 11 of their papers we have counts for
14 papers
On the minimum number of eigenvalues of matrices associated with cographs
Luiz Emilio Allem, Martin Fürer, Carlos Hoppen +2
A symmetric matrix is said to be associated with an -vertex graph with vertex set if, for every $i \neq j…
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 of homogeneous communities in the dense regime, and we introduce a spectral clusteri…
The minimum number of distinct eigenvalues of a threshold graph is at most
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 . Moreover, given any threshold graph and any nonzero real number , w…
On the minimum number of eigenvalues of trees of diameter seven
Luiz Emilio Allem, Carlos Hoppen, Lucas Siviero Sibemberg
The underlying graph of a symmetric matrix is the graph with vertex set such that a pair with $i\neq j…
Diminimal families of arbitrary diameter
Luiz Emilio Allem, Rodrigo Orsini Braga, Carlos Hoppen +3
Given a tree , let be the minimum number of distinct eigenvalues in a symmetric matrix whose underlying graph is . It is well known that , where $d(T)…
On I-eigenvalue free threshold graphs
Luiz Emilio Allem, Elismar R. Oliveira, Fernando Tura
A graph is said to be I-eigenvalue free if it has no eigenvalues in the interval I with respect to the adjacency matrix A. In this paper we present two algorithms for generating I-…