Zobrazeno 1 - 10
of 217
pro vyhledávání: '"Coutinho, Gabriel"'
Autor:
Cançado, Frederico, Coutinho, Gabriel
Whenever graphs admit equitable partitions, their quotient graphs highlight the structure evidenced by the partition. It is therefore very natural to ask what can be said about two graphs that have the same quotient according to certain equitable par
Externí odkaz:
http://arxiv.org/abs/2411.09157
In this paper we prove a conjecture by Wocjan, Elphick and Anekstein (2018) which upper bounds the sum of the squares of the positive (or negative) eigenvalues of the adjacency matrix of a graph by an expression that behaves monotonically in terms of
Externí odkaz:
http://arxiv.org/abs/2411.08184
Autor:
Coutinho, Gabriel, Guo, Krystal
Quantum walks on graphs are fundamental to quantum computing and have led to many interesting open problems in algebraic graph theory. This review article highlights three key classes of open problems in this domain; perfect state transfer, instantan
Externí odkaz:
http://arxiv.org/abs/2404.02236
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. Computing the Grundy number of a graph is an NP-Hard problem. There is a c
Externí odkaz:
http://arxiv.org/abs/2401.03042
Autor:
Coutinho Gabriel, Guo Krystal
Publikováno v:
Special Matrices, Vol 12, Iss 1, Pp 781-793 (2024)
Quantum walks on graphs are fundamental to quantum computing and have led to many interesting open problems in algebraic graph theory. This review article highlights three key classes of open problems in this domain: perfect state transfer, instantan
Externí odkaz:
https://doaj.org/article/77cbb504a1ca460c9215b1383f09f069
The (standard) average mixing matrix of a continuous-time quantum walk is computed by taking the expected value of the mixing matrices of the walk under the uniform sampling distribution on the real line. In this paper we consider alternative probabi
Externí odkaz:
http://arxiv.org/abs/2308.16378
Autor:
Coutinho, Gabriel, Spier, Thomás Jung
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 by the vector chromatic number, resolving a conjecture by Wocjan, Elp
Externí odkaz:
http://arxiv.org/abs/2308.04475
We prove that the only trees that admit perfect state transfer according to the adjacency matrix model are $P_2$ and $P_3$. This answers a question first asked by Godsil in 2012 and proves a conjecture by Coutinho and Liu from 2015.
Externí odkaz:
http://arxiv.org/abs/2305.10199
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 supported in the end vertices of the path which are too close to each
Externí odkaz:
http://arxiv.org/abs/2305.09406
We provide a characterization of perfect state transfer in a quantum walk whose Hamiltonian is given by the normalized Laplacian. We discuss a connection between classical random walks and quantum walks only present in this model, and we also rule ou
Externí odkaz:
http://arxiv.org/abs/2209.04668