Luiz Emilio Allem
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Luiz Emilio Allem has a total of 52 co-authors. Here are the top co-authors by number of shared publications:
- Vilmar Trevisan
Instituto de Matemática e Estatística Universidade Federal do Rio Grande do Sul Porto Alegre Brasil
10 shared publications - Carlos Hoppen
Instituto de Matemática e Estatística, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil
9 shared publications - Lucas Siviero Sibemberg
Instituto de Matemática e Estatística, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil
6 shared publications - Fernando Colman Tura
Departamento de Matemática, UFSM, Santa Maria, Brazil
5 shared publications - Juliane Capaverde
Universidade Federal do Rio Grande do Sul (UFRGS)
3 shared publications - Antonio Cafure
Instituto del Desarrollo Humano, Universidad Nacional de General Sarmiento, Argentina Depto. de Matemática, CBC, Universidad de Buenos Aires, Argentina
2 shared publications
Latest Publications
- Open Access
- 23 October 2026
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 755, 125-150
Spectral characterization of uniform starlike type trees
- 23 October 2026
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 755, 125-150
Open AccessSpectral characterization of uniform starlike type trees
- Open Access
On the minimum number of eigenvalues of matrices associated with cographs
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.Open AccessOn the minimum number of eigenvalues of matrices associated with cographs
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. - 18 July 2025
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 726, 32-53
The minimum number of distinct eigenvalues of a threshold graph is at most 4
- 18 July 2025
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 726, 32-53
The minimum number of distinct eigenvalues of a threshold graph is at most 4
- 28 June 2025
- Published by Springer Nature in Computational and Applied Mathematics
- Vol. 44 (7) , 1-24
A self-adjusting spectral clustering algorithm
- 28 June 2025
- Published by Springer Nature in Computational and Applied Mathematics
- Vol. 44 (7) , 1-24
A self-adjusting spectral clustering algorithm
- Open AccessThe minimum number of distinct eigenvalues of a threshold graph is at most $4$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 $λ$, we explicitly construct a matrix $M$ associated with $G$ such that DSpec$(M)\subseteq\{-λ,0,λ,2λ\}$.Open AccessThe minimum number of distinct eigenvalues of a threshold graph is at most $4$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 $λ$, we explicitly construct a matrix $M$ associated with $G$ such that DSpec$(M)\subseteq\{-λ,0,λ,2λ\}$.
- Open Access
- 20 January 2025
- Published by Brazilian Society for Computational and Applied Mathematics (SBMAC) in Proceeding Series of the Brazilian Society of Computational and Applied Mathematics
- Vol. 11 (1) , 1-7
Short note on the minimum number of distinct eigenvalues of unicyclic graphs
Let q(G) be the minimum number of distinct eigenvalues taken over all real symmetric matrices whose underlying graph is G. Using a linear time algorithm that diagonalizes any symmetric matrix associated to a unicyclic graph, we investigate the maximum eigenvalue multiplicity for these graphs. As an application, we determine the value of q(G) for some family of tadpole graphs, which are unicyclic graphs formed by adding an edge between a cycle and a path.
- 20 January 2025
- Published by Brazilian Society for Computational and Applied Mathematics (SBMAC) in Proceeding Series of the Brazilian Society of Computational and Applied Mathematics
- Vol. 11 (1) , 1-7
Open AccessShort note on the minimum number of distinct eigenvalues of unicyclic graphs
Let q(G) be the minimum number of distinct eigenvalues taken over all real symmetric matrices whose underlying graph is G. Using a linear time algorithm that diagonalizes any symmetric matrix associated to a unicyclic graph, we investigate the maximum eigenvalue multiplicity for these graphs. As an application, we determine the value of q(G) for some family of tadpole graphs, which are unicyclic graphs formed by adding an edge between a cycle and a path.
- Open Access
- 7 April 2023
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 30 (2) , P2.30
Generating $I$-Eigenvalue Free Threshold Graphs
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 twoalgorithms for generating $I$-eigenvalue free threshold graphs.- 7 April 2023
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 30 (2) , P2.30
Open AccessGenerating $I$-Eigenvalue Free Threshold Graphs
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 twoalgorithms for generating $I$-eigenvalue free threshold graphs. - Open Access
Diminimal families of arbitrary diameter
Given a tree $T$, let $q(T)$ be the minimum number of distinct eigenvalues in a symmetric matrix whose underlying graph is $T$. It is well known that $q(T)\geq d(T)+1$, where $d(T)$ is the diameter of $T$, and a tree $T$ is said to be diminimal if $q(T)=d(T)+1$. In this paper, we present families of diminimal trees of any fixed diameter. Our proof is constructive, allowing us to compute, for any diminimal tree $T$ of diameter $d$ in these families, a symmetric matrix $M$ with underlying graph $T$ whose spectrum has exactly $d+1$ distinct eigenvalues.Open AccessDiminimal families of arbitrary diameter
Given a tree $T$, let $q(T)$ be the minimum number of distinct eigenvalues in a symmetric matrix whose underlying graph is $T$. It is well known that $q(T)\geq d(T)+1$, where $d(T)$ is the diameter of $T$, and a tree $T$ is said to be diminimal if $q(T)=d(T)+1$. In this paper, we present families of diminimal trees of any fixed diameter. Our proof is constructive, allowing us to compute, for any diminimal tree $T$ of diameter $d$ in these families, a symmetric matrix $M$ with underlying graph $T$ whose spectrum has exactly $d+1$ distinct eigenvalues. - Open Access
- 8 December 2022
- Published by Brazilian Society for Computational and Applied Mathematics (SBMAC) in Proceeding Series of the Brazilian Society of Computational and Applied Mathematics
- Vol. 9 (1)
Hierarchical Similarity Measure for Spectral Clustering
Hierarchical Similarity Measure for Spectral Clustering
- 8 December 2022
- Published by Brazilian Society for Computational and Applied Mathematics (SBMAC) in Proceeding Series of the Brazilian Society of Computational and Applied Mathematics
- Vol. 9 (1)
Open AccessHierarchical Similarity Measure for Spectral Clustering
Hierarchical Similarity Measure for Spectral Clustering
- Open Access
- 8 November 2022
- Published by Brazilian Society for Computational and Applied Mathematics (SBMAC) in Trends in Computational and Applied Mathematics
- Vol. 23 (4) , 705-729
A Spectral Clustering Approach for the Evolution of the COVID-19 Pandemic in the State of Rio Grande do Sul, Brazil
The aim of this paper is to analyse the evolution of the COVID-19 pandemic in Rio Grande do Sul by applying graph-theoretical tools, particularly spectral clustering techniques, on weighted graphs defined on the set of 167 municipalities in the state with population 10,000 or more, which are based on data provided by government agencies and other sources. To respond to this outbreak, the state has adopted a system by which pre-determined regions are assigned flags on a weekly basis, and different measures go into effect according to the flag assigned. Our results suggest that considering a flexible approach to the regions themselves might be a useful additional tool to give more leeway to cities with lower incidence rates, while keeping the focus on public safety. Moreover, simulations show that the combination of pendulum migration and isolation data used in this paper leads to a coherent qualitative description of the evolution of the pandemic in Rio Grande do Sul. These simulations also confirm the dampening effect of isolation on the dissemination of the disease.
- 8 November 2022
- Published by Brazilian Society for Computational and Applied Mathematics (SBMAC) in Trends in Computational and Applied Mathematics
- Vol. 23 (4) , 705-729
Open AccessA Spectral Clustering Approach for the Evolution of the COVID-19 Pandemic in the State of Rio Grande do Sul, Brazil
The aim of this paper is to analyse the evolution of the COVID-19 pandemic in Rio Grande do Sul by applying graph-theoretical tools, particularly spectral clustering techniques, on weighted graphs defined on the set of 167 municipalities in the state with population 10,000 or more, which are based on data provided by government agencies and other sources. To respond to this outbreak, the state has adopted a system by which pre-determined regions are assigned flags on a weekly basis, and different measures go into effect according to the flag assigned. Our results suggest that considering a flexible approach to the regions themselves might be a useful additional tool to give more leeway to cities with lower incidence rates, while keeping the focus on public safety. Moreover, simulations show that the combination of pendulum migration and isolation data used in this paper leads to a coherent qualitative description of the evolution of the pandemic in Rio Grande do Sul. These simulations also confirm the dampening effect of isolation on the dissemination of the disease.