5 citations · 22 across the 23 of their papers we have counts for
6 papers · 1 filter
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…
Effects of Backtracking on PageRank
Cory Glover, Tyler Jones, Mark Kempton +1
In this paper, we consider three variations on standard PageRank: Non-backtracking PageRank, -PageRank, and -PageRank, all of which alter the standard formula by adjusti…
On the Laplacian spread of digraphs
Wayne Barrett, Thomas R. Cameron, Emily Evans +2
In this article, we extend the notion of the Laplacian spread to simple directed graphs (digraphs) using the restricted numerical range. First, we provide Laplacian spread values f…
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…