32 citations · 173 across the 34 of their papers we have counts for
35 papers · 1 filter
Cubic graphs with no eigenvalues in the interval (-1,1)
Krystal Guo, Gordon F. Royle
We give a complete characterisation of the cubic graphs with no eigenvalues in the open interval . There are two infinite families, one due to Guo and Mohar [Linear Algebra…
Separating rank 3 graphs
John Bamberg, Michael Giudici, Jesse Lansdown +1
We classify, up to some notoriously hard cases, the rank 3 graphs which fail to meet either the Delsarte or the Hoffman bound. As a consequence, we resolve the question of separati…
Tournaments and Even Graphs are Equinumerous
Gordon F. Royle, Cheryl E. Praeger, S. P. Glasby +2
A graph is called odd if there is an orientation of its edges and an automorphism that reverses the sense of an odd number of its edges, and even otherwise. Pontus von Brömssen (né…
There are only a finite number of excluded minors for the class of bicircular matroids
Matt DeVos, Daryl Funk, Luis Goddyn +1
We show that the class of bicircular matroids has only a finite number of excluded minors. Key tools used in our proof include representations of matroids by biased graphs and the…
On the flip graphs on perfect matchings of complete graphs and signed reversal graphs
Sebastian M. Cioabă, Gordon Royle, Zhao Kuang Tan
In this paper, we study the flip graph on the perfect matchings of a complete graph of even order. We investigate its combinatorial and spectral properties including connections to…
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…