4 papers
Spectral upper bounds for the Grundy number of a graph
Thiago Assis, Gabriel Coutinho, Emanuel Juliano
The Grundy number of a graph is the minimum number of colors needed to properly color the graph using the first-fit greedy algorithm regardless of the initial vertex ordering. Comp…
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…
Quantum walks do not like bridges
Gabriel Coutinho, Chris Godsil, Emanuel Juliano +1
We consider graphs with two cut vertices joined by a path with one or two edges, and prove that there can be no quantum perfect state transfer between these vertices, unless the gr…