24 citations · 35 across the 12 of their papers we have counts for
14 papers · 1 filter
The Spectral Theory of Threshold Graphs: A Survey
Pallabi Manna, Santanu Mandal, Fernando C. Tura
Threshold graphs-the -free graphs, equivalently those built from a single vertex by repeatedly adding isolated or dominating vertices-are among the most thoroug…
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…
A linear algorithm for obtaining the Laplacian eigenvalues of a cograph
Guantao Chen, Fernando C. Tura
In this paper, we give a linear algorithm for obtaining the Laplacian eigenvalues of a cograph. This approach is more efficient as there is no need to directly compute the eigenval…
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-…
Laplacian eigenvalues of equivalent cographs
J. Lazzarin, O. F. Márquez, F. C. Tura
Let G and H be equivalent cographs with their reduction R_G and R_H, and suppose the vertices of R_G and R_H are labeled by the twin numbers t_i of the k twin classes they represen…
A conjecture of eigenvalues of threshold graphs
Fernando Tura
Let be the anti-regular graph of order It was conjectured that among all threshold graphs on vertices, has the smallest positive eigenvalue and the largest eig…
On the eccentricity energy of complete mutipartite graph
Fernando Tura
The eccentricity (anti-adjacency) matrix of a graph is obtained from the distance matrix by retaining the eccentricities in each row and each column. The $\var…
Integral cographs and applications
Luiz Emilio Allem, Fernando Tura
A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, we show a cograph that has a balanced cotree $T_{G}(a_{1},\ldots,a_{r-1},0|0,…
An explicit formula for the distance characteristic polynomial of threshold graphs
Joao Lazzarin, Oscar F. Marquez, Fernando C. Tura
A threshold graph G on n vertices is defined by binary sequence of length n. In this paper we present an explicit formula for computing the distance characteristic polynomial of a…
More on Equienergetic Threshold Graphs
Fernando Tura
The energy of a graph is defined as the sum the absolute values of the eigenvalues of its adjacency matrix. A threshold graph G on n vertices is coded by a binary sequence of lengt…
No Threshold graphs are cospectral
J. Lazzarin, O. F. Márquez, F. Tura
A threshold graph G on n vertices is defined by binary sequence of length n. In this paper we present an explicit formula for computing the characteristic polynomial of a threshold…
Multiplicity of eigenvalues of cographs
Luiz Emilio Allem, Fernando Tura
Motivated by the linear time algorithm that locates the eigenvalues of a cograph G [10], we investigate the multiplicity of eigenvalue for λ\neq -1,0. For cographs with balanced co…
Eigenvalue location in cographs
David P. Jacobs, Vilmar Trevisan, Fernando C. Tura
We give an time and space algorithm for constructing a diagonal matrix congruent to A+xI, where A is the adjacency matrix of a cograph and . Applications in…
Counting Spanning trees in double nested graphs
Fernando Tura
In this paper we give a linear time algorithm for computing the number of spanninig trees in double nested graphs.