5 papers
Threshold Graphs Allow Few Distinct Eigenvalues: A New Approach
Jane Breen, Shaun Fallat, Johnna Parenteau
For any graph , we associate a family of real symmetric matrices, , where for any , the location of the nonzero off-diagonal entries of are governed by the…
Kemeny's constant and Braess cliques in graphs
Jane Breen, Emma deBlieck, Kevin N. Vander Meulen
Kemeny's constant is used as a measure of the average travel time on a graph. Braess' paradox for graphs is the observation that in some graphs, when an edge is added, Kemeny's con…
On defining Kemeny's constant for non-backtracking random walks
Jane Breen, Mark Kempton, Adam Knudson +1
We propose two possible definitions for a version of Kemeny's constant of a graph based on non-backtracking random walks (in place of the usual simple random walk). We show that th…
Reinforcement learning for graph theory, Parallelizing Wagner's approach
Alix Bouffard, Jane Breen
Our work applies reinforcement learning to construct counterexamples concerning conjectured bounds on the spectral radius of the Laplacian matrix of a graph. We expand upon the re-…
Threshold graphs, Kemeny's constant, and related random walk parameters
Jane Breen, Sooyeong Kim, Alexander Low Fung +3
Kemeny's constant measures how fast a random walker moves around in a graph. Expressions for Kemeny's constant can be quite involved, and for this reason, many lines of research fo…