7 citations · 11 across the 8 of their papers we have counts for
12 papers · 1 filter
Total Conformal Rigidity in Graphs
Henrique Assumpção, Gabriel Coutinho, Chris Godsil
We introduce and study a generalization of conformal rigidity for graphs. A graph is -conformally rigid if the uniform edge weights simultaneously maximize the sum of the sm…
Sums of squares of eigenvalues and the vector chromatic number
Gabriel Coutinho, Thomás Jung Spier
In this short paper we prove that the sum of the squares of negative (or positive) eigenvalues of the adjacency matrix of a graph is lower bounded by the sum of the degrees divided…
No perfect state transfer in trees with more than 3 vertices
Gabriel Coutinho, Emanuel Juliano, Thomás Jung Spier
We prove that the only trees that admit perfect state transfer according to the adjacency matrix model are and . This answers a question first asked by Godsil in 2012 an…
The spectrum of symmetric decorated paths
Gabriel Coutinho, Emanuel Juliano, Thomás Jung Spier
The main result of this paper states that in a rooted product of a path with rooted graphs which are disposed in a somewhat mirror-symmetric fashion, there are distinct eigenvalues…
Fundamentals of fractional revival in graphs
Ada Chan, Gabriel Coutinho, Whitney Drazen +6
We develop a general spectral framework to analyze quantum fractional revival in quantum spin networks. In particular, we introduce generalizations of the notions of cospectral and…
Colouring the normalized Laplacian
Gabriel Coutinho, Rafael Grandsire, Célio Passos
We apply Cauchy's interlacing theorem to derive some eigenvalue bounds to the chromatic number using the normalized Laplacian matrix, including a combinatorial characterization of…