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pro vyhledávání: '"Godsil, Chris"'
Autor:
Godsil, Chris, Sun, Wanting
The degree matrix of a graph is the diagonal matrix with diagonal entries equal to the degrees of the vertices of $X$. If $X_1$ and $X_2$ are graphs with respective adjacency matrices $A_1$ and $A_2$ and degree matrices $D_1$ and $D_2$, we say that $
Externí odkaz:
http://arxiv.org/abs/2407.11328
Autor:
Godsil, Chris, Zhang, Xiaohong
Let $G$ be a finite abelian group. Bridges and Mena characterized the Cayley graphs of $G$ that have only integer eigenvalues. Here we consider the $(0,1,-1)$ adjacency matrix of an oriented Cayley graph or of a signed Cayley graph $X$ on $G$. We giv
Externí odkaz:
http://arxiv.org/abs/2405.14140
Autor:
Godsil, Chris, Sobchuk, Mariia
We construct a new graph on 120 vertices whose quantum and classical independence numbers are different. At the same time, we construct an infinite family of graphs whose quantum chromatic numbers are smaller than the classical chromatic numbers. Fur
Externí odkaz:
http://arxiv.org/abs/2401.16518
A graph is called integral if all its eigenvalues are integers. A Cayley graph is called normal if its connection set is a union of conjugacy classes. We show that a non-empty integral normal Cayley graph for a group of odd order has an odd eigenvalu
Externí odkaz:
http://arxiv.org/abs/2310.09058
Let $M\circ N$ denote the Schur product of two matrices $M$ and $N$. A graph $X$ with adjacency matrix $A$ is walk regular if $A^k\circ I$ is a constant times $I$ for each $k\ge0$, and $X$ is 1-walk-regular if it is walk regular and $A^k\circ A$ is a
Externí odkaz:
http://arxiv.org/abs/2302.03854
Autor:
Acuaviva, Antonio, Chan, Ada, Eldridge, Summer, Godsil, Chris, How-Chun-Lun, Matthew, Tamon, Christino, Wright, Emily, Zhang, Xiaohong
Given a graph with Hermitian adjacency matrix $H$, perfect state transfer occurs from vertex $a$ to vertex $b$ if the $(b,a)$-entry of the unitary matrix $\exp(-iHt)$ has unit magnitude for some time $t$. This phenomenon is relevant for information t
Externí odkaz:
http://arxiv.org/abs/2301.01473
Autor:
Coutinho, Gabriel, Baptista, Pedro Ferreira, Godsil, Chris, Spier, Thomás Jung, Werner, Reinhard
The adjacency matrix of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. Although the entries of the adjacency matrix are integers, its eigenvalues are generally irrational and, because of this, the behaviour of t
Externí odkaz:
http://arxiv.org/abs/2208.08971
In this paper, we introduce a discrete quantum walk model called bipartite walks. Bipartite walks include many known discrete quantum walk models, like arc-reversal walks, vertex-face walks. For the transition matrix of a quantum walk, there is a Ham
Externí odkaz:
http://arxiv.org/abs/2207.01673
Publikováno v:
Quantum Information Processing 22, 8 (2023)
In this paper, we characterize perfect state transfer in Cayley graphs for abelian groups that have a cyclic Sylow-2-subgroup. This generalizes a result of Ba\v{s}i\'c from 2013 where he provides a similar characterization for Cayley graphs of cyclic
Externí odkaz:
http://arxiv.org/abs/2204.09802