Krystal Guo

activity

20102026

most citedPerfect state transfer on distance-regular graphs and association schemes

72 citations · 112 across the 21 of their papers we have counts for

collaborators

27 papers

math.CO2026

Sustainable trees

Ferenc Bencs, Maarten van Dijk, Krystal Guo

Let $X$ be a connected graph and let $λ_{1} (X)$ denote the spectral radius of its adjacency matrix. An edge $e$ of $X$ is sustainable if it can be deleted and replaced by a non-edge…

math.CO2026

Seymour-tight orientations

Krystal Guo, Ross J. Kang, Gabriëlle Zwaneveld

We investigate `almost counterexamples' to Seymour's second neighbourhood conjecture. In what we call Seymour-tight orientations, the size of the first neighbourhood of each vertex…

math.CO2025

On cores of distance-regular graphs

Annemarie Geertsema, Chris Godsil, Krystal Guo

We look at the question of which distance-regular graphs are core-complete, meaning they are isomorphic to their own core or have a complete core. We build on Roberson's homomorphi…

math.CO2023★ 4 cited

Positive and Negative Square Energies of Graphs

Aida Abiad, Leonardo de Lima, Dheer Noal Desai +3

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 an…

math.CO2022★ 1 cited

Perfect state transfer in quantum walks on orientable maps

Krystal Guo, Vincent Schmeits

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…

math.CO2022★ 8 cited

New Eigenvalue Bound for the Fractional Chromatic Number

Krystal Guo, Sam Spiro

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 \[χ_f(G…

math.CO2022

Pseudo-Geometric Strongly Regular Graphs with a Regular Point

Edwin van Dam, Krystal Guo

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 s…

math-ph2020★ 10 cited

Entanglement of Free Fermions on Hadamard Graphs

Nicolas Crampe, Krystal Guo, Luc Vinet

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 gro…

math.CO2020★ 3 cited

Simple eigenvalues of cubic vertex-transitive graphs

Krystal Guo, Bojan Mohar

If $v$ is an eigenvector for eigenvalue $λ$ of a graph $X$ and $α$ is an automorphism of $X$ , then $α (v)$ is also an eigenvector for $λ$ . Thus it is rather exceptional for an eigen…

math.CO2019★ 1 cited

Diagonal entries of the average mixing matrix

Chris Godsil, Krystal Guo, Mariia Sobchuk

We study the diagonal entries of the average mixing matrix of continuous quantum walks. The average mixing matrix is a graph invariant; it is the sum of the Schur squares of spectr…

math.CO2019

Transversal polynomial of r-fold covers

Chris Godsil, Krystal Guo, Gordon Royle

We explore the interplay between algebraic combinatorics and algorithmic problems in graph theory by defining a polynomial with connections to correspondence colouring (also known…

math.CO2018

The biclique covering number of grids

Krystal Guo, Tony Huynh, Marco Macchia

We determine the exact value of the biclique covering number for all grid graphs.

math.CO2018★ 4 cited

The chromatic index of strongly regular graphs

Sebastian M. Cioaba, Krystal Guo, Willem H. Haemers

We determine (partly by computer search) the chromatic index (edge-chromatic number) of many strongly regular graphs (SRGs), including the SRGs of degree $k \leq 18$ and their comp…

math.CO2018

Short rainbow cycles in graphs and matroids

Matt DeVos, Matthew Drescher, Daryl Funk +5

Let $G$ be a simple $n$ -vertex graph and $c$ be a colouring of $E (G)$ with $n$ colours, where each colour class has size at least $2$ . We prove that $(G, c)$ contains a rainbow cycl…

math.CO2018★ 1 cited

Partially ordering the class of invertible trees

Krystal Guo

A tree T is invertible if and only if T has a perfect matching. Godsil considers an invertible tree T and finds that the inverse of the adjacency matrix of T has entries in {0, 1,…

math.CO2018

Using the existence of t-designs to prove Erdős-Ko-Rado

Chris Godsil, Krystal Guo

In 1984, Wilson proved the Erdős-Ko-Rado theorem for $t$ -intersecting families of $k$ -subsets of an $n$ -set: he showed that if $n \geq (t + 1) (k - t + 1)$ and $F$ is a family of $…

math.CO2017

State transfer in strongly regular graphs with an edge perturbation

Chris Godsil, Krystal Guo, Mark Kempton +1

Quantum walks, an important tool in quantum computing, have been very successfully investigated using techniques in algebraic graph theory. We are motivated by the study of state t…

math.CO2017

Average mixing matrix of trees

Chris Godsil, Krystal Guo, John Sinkovic

We investigate the rank of the average mixing matrix of trees, with all eigenvalues distinct. The rank of the average mixing matrix of a tree on $n$ vertices with $n$ distinct eige…

math.CO2017★ 1 cited

A New Perspective on the Average Mixing Matrix

Gabriel Coutinho, Chris Godsil, Krystal Guo +1

We consider the continuous-time quantum walk defined on the adjacency matrix of a graph. At each instant, the walk defines a mixing matrix which is doubly-stochastic. The average o…

quant-ph2016

Pretty good state transfer between internal nodes of paths

Gabriel Coutinho, Krystal Guo, Christopher M. van Bommel

We study a continous-time quantum walk on a path graph. In this paper, we show that, for any odd prime $p$ and positive integer $t$ , the path on $2^{t} p - 1$ vertices admits pretty…

math.CO2016

Cycle Spaces of Digraphs

Chris Godsil, Krystal Guo

The cycle space of a graph corresponds to the kernel of an incidence matrix. We investigate an analogous subspace for digraphs. In the case of digraphs of graphs, where every edge…

math.CO2015

Spectral bound for separations in Eulerian digraphs

Krystal Guo

The spectra of digraphs, unlike those of graphs, is a relatively unexplored territory. In a digraph, a separation is a pair of sets of vertices X and Y such that there are no arcs…

math.CO2015

Quantum Walks on Generalized Quadrangles

Chris Godsil, Krystal Guo, Tor G. J. Myklebust

We study the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum of $S^{+} (U^{3})$ , a matrix…

math.CO2015★ 7 cited

Hermitian adjacency matrix of digraphs and mixed graphs

Krystal Guo, Bojan Mohar

The paper gives a thorough introduction to spectra of digraphs via its Hermitian adjacency matrix. This matrix is indexed by the vertices of the digraph, and the entry correspondin…