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of 82
pro vyhledávání: '"Guo, Krystal"'
Autor:
Guo, Krystal, Royle, Gordon F.
We give a complete characterisation of the cubic graphs with no eigenvalues in the open interval $(-1,1)$. There are two infinite families, one due to Guo and Mohar [Linear Algebra Appl. 449:68--75] the other due to Koll\'ar and Sarnak [Communication
Externí odkaz:
http://arxiv.org/abs/2409.02678
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
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
Autor:
Abiad, Aida, de Lima, Leonardo, Desai, Dheer Noal, Guo, Krystal, Hogben, Leslie, Madrid, Jose
The energy of a graph $G$ is the sum of the absolute values of the eigenvalues of the adjacency matrix of $G$. Let $s^+(G), s^-(G)$ denote the sum of the squares of the positive and negative eigenvalues of $G$, respectively. It was conjectured by [El
Externí odkaz:
http://arxiv.org/abs/2303.11930
Autor:
Guo, Krystal, Schmeits, Vincent
A discrete-time quantum walk is the quantum analogue of a Markov chain on a graph. Zhan [J. Algebraic Combin. 53(4):1187-1213, 2020] proposes a model of discrete-time quantum walk whose transition matrix is given by two reflections, using the face an
Externí odkaz:
http://arxiv.org/abs/2211.12841
Autor:
Guo, Krystal, Spiro, Sam
Given a graph $G$, we let $s^+(G)$ denote the sum of the squares of the positive eigenvalues of the adjacency matrix of $G$, and we similarly define $s^-(G)$. We prove that \[\chi_f(G)\ge 1+\max\left\{\frac{s^+(G)}{s^-(G)},\frac{s^-(G)}{s^+(G)}\right
Externí odkaz:
http://arxiv.org/abs/2211.04499
Autor:
van Dam, Edwin, Guo, Krystal
We study pseudo-geometric strongly regular graphs whose second subconstituent with respect to a vertex is a cover of a strongly regular graph or a complete graph. By studying the structure of such graphs, we characterize all graphs containing such a
Externí odkaz:
http://arxiv.org/abs/2204.04755
Publikováno v:
Nuclear Physics B Volume 960, November 2020, 115176
Free Fermions on vertices of distance-regular graphs are considered. Bipartition are defined by taking as one part all vertices at a given distance from a reference vertex. The ground state is constructed by filling all states below a certain energy.
Externí odkaz:
http://arxiv.org/abs/2008.04925
Autor:
Guo, Krystal, Mohar, Bojan
If $v$ is an eigenvector for eigenvalue $\lambda$ of a graph $X$ and $\alpha$ is an automorphism of $X$, then $\alpha(v)$ is also an eigenvector for $\lambda$. Thus it is rather exceptional for an eigenvalue of a vertex-transitive graph to be simple.
Externí odkaz:
http://arxiv.org/abs/2002.05694
We explore the interplay between algebraic combinatorics and algorithmic problems in graph theory by defining a polynomial with connections to correspondence colouring (also known as DP-colouring), a recent generalization of list-colouring, and the U
Externí odkaz:
http://arxiv.org/abs/1910.05478