5 citations · 15 across the 9 of their papers we have counts for
18 papers
Isospectral reductions and quantum walks on graphs
Mark Kempton, John Tolbert
We give a new formula for computing the isospectral reduction of a matrix (and graph) down to a submatrix (or subgraph). Using this, we generalize the notion of isospectral reducti…
Unicyclic graphs and the inertia of the distance squared matrix
Christian Howell, Mark Kempton, Kellon Sandall +1
A result of Bapat and Sivasubramanian gives the inertia of the distance squared matrix of a tree. We develop general tools on how pendant vertices and degree 2 vertices affect the…
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…
New conjectures on algebraic connectivity and the Laplacian spread of graphs
Wayne Barrett, Emily Evans, H. Tracy Hall +1
We conjecture a new lower bound on the algebraic connectivity of a graph that involves the number of vertices of high eccentricity in a graph. We prove that this lower bound implie…
A 1-Separation Formula for the Graph Kemeny Constant and Braess Edges
Nolan Faught, Mark Kempton, Adam Knudson
Kemeny's constant of a simple connected graph is the expected length of a random walk from to any given vertex . We provide a simple method for computing Kemeny's…
Spectral properties of the non-backtracking matrix of a graph
Cory Glover, Mark Kempton
We investigate the spectrum of the non-backtracking matrix of a graph. In particular, we show how to obtain eigenvectors of the non-backtracking matrix in terms of eigenvectors of…