5 papers · 1 filter
Kemeny's constant for a graph with bridges
Jane Breen, Emanuele Crisostomi, Sooyeong Kim
In this paper, we determine a formula for Kemeny's constant for a graph with multiple bridges, in terms of quantities that are inherent to the subgraphs obtained upon removal of al…
Kemeny's constant for non-backtracking random walks
Jane Breen, Nolan Faught, Cory Glover +3
Kemeny's constant for a connected graph is the expected time for a random walk to reach a randomly-chosen vertex , regardless of the choice of the initial vertex. We extend…
Maximum spread of graphs and bipartite graphs
Jane Breen, Alex W. N. Riasanovsky, Michael Tait +1
Given any graph , the (adjacency) spread of is the maximum absolute difference between any two eigenvalues of the adjacency matrix of . In this paper, we resolve a pair o…
Hadamard diagonalizable graphs of order at most 36
Jane Breen, Steve Butler, Melissa Fuentes +7
If the Laplacian matrix of a graph has a full set of orthogonal eigenvectors with entries , then the matrix formed by taking the columns as the eigenvectors is a Hadamard mat…
Optimizing the trade-off between number of cops and capture time in Cops and Robbers
Anthony Bonato, Jane Breen, Boris Brimkov +6
The cop throttling number of a graph for the game of Cops and Robbers is the minimum of , where is the number of cops and is the minimu…