Research

Publications

Markov chains and random walks on graphs

• Sooyeong Kim, Jane Breen, Ekaterina Dudkina, Federico Poloni, Emanuele Crisostomi. On the effectiveness of random walks for modeling epidemics on networks. PLOS One (accepted, in press).

• Jane Breen, Nolan Faught, Cory Glover, Mark Kempton, Adam Knudson, Alice Oveson. Kemeny's constant for non-backtracking random walks.  Random Structures and Algorithms (accepted, in press).

• Jane Breen, Emanuele Crisostomi, Sooyeong Kim. Kemeny's constant for a graph with bridges. Discrete Applied Mathematics 322 (2022), 20--35.

• Jane Breen, Steve Kirkland. A structured condition number for Kemeny's constant. SIAM Journal of Matrix Analysis and its Applications 40:4 (2019), 1555--1578.

• Jane Breen, Steve Butler, Nicklas Day, Colt DeArmond, Kate Lorenzen, Haoyang Qian, Jacob Riesen. Computing Kemeny's constant for barbell-type graphs. Electronic Journal of Linear Algebra 35 (2019), 583--598.

• Jane Breen, Emanuele Crisostomi, Mahsa Faizrahnemoon, Steve Kirkland, Robert Shorten. Clustering behaviour in Markov chains with eigenvalues close to one. Linear Algebra and its Applications 555 (2018), 163--185.

• Jane Breen, Steve Kirkland. Minimising the largest mean first passage time of a Markov chain: The influence of directed graphs. Linear Algebra and its Applications, 520 (2017), 306--334.

• Jane Breen, Steve Kirkland. Stationary vectors of stochastic matrices subject to combinatorial constraints. Electronic Journal of Linear Algebra, 28 (2015), 25--53. 

Spectral graph theory

• Jane Breen, Alex W. N. Riasanovsky, Michael Tait, John C. Urschel. Maximum spread of graphs and bipartite graphs. Comm. Amer. Math. Soc. 2 (2022), 417--480.

• Aida Abiad, Jane Breen, Boris Brimkov, Thomas R. Cameron, Himanshu Gupta, Ralihe R. Villagrán.  Constructions of cospectral graphs with different zero forcing numbers. The Electronic Journal of Linear Algebra 38 (2022), 280--294.

• Jane Breen, Steve Butler, Melissa Fuentes, Bernard Lidicky, Michael Phillips, Alexander W.N. Riasanovsky, Sung-Yell Song, Ralihe R. Villagrán, Cedar Wiseman, Xiaohong Zhang. Hadamard diagonalizable graphs of order at most 36. The Electronic Journal of Combinatorics (accepted, in press).

Miscellaneous

• Jane Breen, Carraugh Brouwer, Minnie Catral, Michael Cavers, Pauline van den Driessche, Kevin Vander Meulen. Minimum number of distinct eigenvalues allowed by a sign pattern. Linear Algebra and its Applications 654 (2022), 311--338.

• Anthony Bonato, Jane Breen, Boris Brimkov, Joshua Carlson, Sean English, Jesse Geneson, Leslie Hogben, K. E. Perry, Carolyn Reinhart. Optimizing the trade-off between number of cops and capture time in Cops and Robbers. Journal of Combinatorics 13:1 (2022), 79--203.

• Jane Breen, Boris Brimkov, Joshua Carlson, Leslie Hogben, K.E. Perry, Carolyn Reinhart. Throttling for the game of Cops and Robbers on graphs. Discrete Mathematics 341:9 (2018), 2418--2430.