5 citations · 22 across the 23 of their papers we have counts for
35 papers
Pretty good quantum state transfer via transcendental edge weights
Addison Ballif, Mark Kempton, James B. Larsen +3
We prove that if we take a rooted product of a circulant graph with universal perfect state transfer with a path of fixed length whose end edge is weighted with a transcendental nu…
Nordhaus-Gaddum upper bounds for graph connectivity parameters
Mark Kempton, Xavier Zaitzeff, Sibi Muthuprakash
We examine upper bounds on Nordhaus-Gaddum type problems for parameters related to graph connectivity. Our main result is that for a graph on vertices where both and it…
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…
Two Distinct Eigenvalues from a New Graph Product
Eric Culver, Mark Kempton
The parameter of a graph is the minimum number of distinct eigenvalues of a symmetric matrix whose pattern is given by . We introduce a novel graph product by which w…
A Ricci flow on graphs from effective resistance
Aleyah Dawkins, Vishal Gupta, Mark Kempton +4
In this paper, we introduce a new notion of curvature on the edges of a graph that is defined in terms of effective resistances. We call this the Ricci--Foster curvature. We study…
Node resistance curvature in Cartesian graph products
Aleyah Dawkins, Vishal Gupta, Mark Kempton +4
Devriendt and Lambiotte recently introduced the \emph{node resistance curvature}, a notion of graph curvature based on the effective resistance matrix. In this paper, we begin the…
Pretty good fractional revival via magnetic fields: theory and examples
Whitney Drazen, Mark Kempton, Gabor Lippner
We develop the theory of pretty good quantum fractional revival in arbitrary sized subsets of a graph, including the theory for fractional cospectrality of subsets of arbitrary siz…
Bounds on Kemeny's constant of a graph and the Nordhaus-Gaddum problem
Sooyeong Kim, Neal Madras, Ada Chan +3
We study Nordhaus-Gaddum problems for Kemeny's constant of a connected graph . We prove bounds on and the pro…
Kemeny's constant and enumerating Braess edges in trees
Jihyeug Jang, Mark Kempton, Sooyeong Kim +3
We study the problem of enumerating Braess edges for Kemeny's constant in trees. We obtain bounds and asympotic results for the number of Braess edges in some families of trees.
Zero Forcing on 2-connected Outerplanar Graphs
Nolan Ison, Mark Kempton, Franklin Kenter
We determine upper and lower bounds on the zero forcing number of 2-connected outerplanar graphs in terms of the structure of the weak dual. We show that the upper bound is always…
A Nordhaus-Gaddum type problem for the normalized Laplacian spectrum and graph Cheeger constant
J. Nolan Faught, Mark Kempton, Adam Knudson
For a graph on vertices with normalized Laplacian eigenvalues and graph complement , we prove that \begin{equation*} \…
Bordering of Symmetric Matrices and an Application to the Minimum Number of Distinct Eigenvalues for the Join of Graphs
Aida Abiad, Shaun M. Fallat, Mark Kempton +5
An important facet of the inverse eigenvalue problem for graphs is to determine the minimum number of distinct eigenvalues of a particular graph. We resolve this question for the j…
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…
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…
SpectralFly: Ramanujan Graphs as Flexible and Efficient Interconnection Networks
Stephen Young, Sinan Aksoy, Jesun Firoz +5
In recent years, graph theoretic considerations have become increasingly important in the design of HPC interconnection topologies. One approach is to seek optimal or near-optimal…
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…
Resistance distance, Kirchhoff index, and Kemeny's constant in flower graphs
Nolan Faught, Mark Kempton, Adam Knudson
We obtain a general formula for the resistance distance (or effective resistance) between any pair of nodes in a general family of graphs which we call flower graphs. Flower graphs…
Approximate quantum fractional revival in paths and cycles
Ada Chan, Whitney Drazen, Or Eisenberg +2
We initiate the study of approximate quantum fractional revival in graphs, a generalization of pretty good quantum state transfer in graphs. We give a complete characterization of…
Fundamentals of fractional revival in graphs
Ada Chan, Gabriel Coutinho, Whitney Drazen +6
We develop a general spectral framework to analyze quantum fractional revival in quantum spin networks. In particular, we introduce generalizations of the notions of cospectral and…