17 citations · 50 across the 28 of their papers we have counts for
5 papers · 1 filter
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-…
Applications of rational difference equations to spectral graph theory: expanded version
Elismar R. Oliveira, Vilmar Trevisan
We study a general class of recurrence relations that appear in the application of a matrix diagonalization procedure. We find general closed formula and determine analytical prope…
Spectral ordering and 2-switch transformations
Elismar R. Oliveira, Victor N. Schvöllner, Vilmar Trevisan
We address the problem of ordering trees with the same degree sequence by their spectral radii. To achieve that, we consider 2-switch transformations which preserve the degree sequ…
Most Laplacian eigenvalues of a tree are small
David P. Jacobs, Elismar R. Oliveira, Vilmar Trevisan
We show that the number of Laplacian eigenvalues greater than the average degree of a tree having vertices is at most .
No two starlikes have equal index
Elismar R. Oliveira, Dragan Stevanović, Vilmar Trevisan
The index of a graph is the largest eigenvalue of its adjacency matrix. A starlike is a tree having a unique vertex of degree . We show how to order the starlike trees with $n…