15 citations · 31 across the 13 of their papers we have counts for
16 papers
Throttling for metric dimension and its variants
Boris Brimkov, Peter Diao, Jesse Geneson +4
Metric dimension is a graph parameter that has been applied to robot navigation and finding low-dimensional vector embeddings. Throttling entails minimizing the sum of two availabl…
Leaky Forcing: Extending Zero Forcing Results to a Fault-Tolerant Setting
Beth Bjorkman, Lei Cao, Franklin Kenter +3
We study a recent variation of zero forcing called leaky forcing. Zero forcing is a propagation process on a network whereby some nodes are initially blue with all others white. Bl…
Defective eigenvalues of the non-backtracking matrix
Kristin Heysse, Kate Lorenzen, Carolyn Reinhart
We consider graphs for which the non-backtracking matrix has defective eigenvalues, or graphs for which the matrix does not have a full set of eigenvectors. The existence of these…
The inverse eigenvalue problem for probe graphs
Emelie Curl, Jürgen Kritschgau, Carolyn Reinhart +1
In this paper, we initiate the study of the inverse eigenvalue problem for probe graphs. A probe graph is a graph whose vertices are partitioned into probe vertices and non-probe v…
On the zero forcing number of the complement of graphs with forbidden subgraphs
Emelie Curl, Shaun Fallat, Ryan Moruzzi +2
Motivated in part by an observation that the zero forcing number for the complement of a tree on vertices is either or in one exceptional case, we consider the zero…
The multi-robber damage number of a graph
Joshua Carlson, Meghan Halloran, Carolyn Reinhart
In many variants of the game of Cops and Robbers on graphs, multiple cops play against a single robber. In 2019, Cox and Sanaei introduced a variant of the game that gives the robb…
Power domination reconfiguration
Beth Bjorkman, Chassidy Bozeman, Daniela Ferrero +5
The study of token addition and removal and token jumping reconfiguration graphs for power domination is initiated. Some results established here can be extended by applying the me…
Spectra of variants of distance matrices of graphs and digraphs: a survey
Leslie Hogben, Carolyn Reinhart
Distance matrices of graphs were introduced by Graham and Pollack in 1971 to study a problem in communications. Since then, there has been extensive research on the distance matric…
The damage throttling number of a graph
Joshua Carlson, Robin Eagleton, Jesse Geneson +3
The cop throttling number of a graph, introduced in 2018 by Breen et al., optimizes the balance between the number of cops used and the number of rounds required to catch the robbe…
Spectral theory of products of digraphs
Minerva Catral, Lorenzo Ciardo, Leslie Hogben +1
A unified approach to the determination of eigenvalues and eigenvectors of specific matrices associated with directed graphs is presented. Matrices studied include the distance 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…
The normalized distance Laplacian
Carolyn Reinhart
The distance matrix of a graph is the matrix containing the pairwise distances between vertices. The transmission of a vertex in is the sum of the di…
Graphs that are cospectral for the distance Laplacian
Boris Brimkov, Ken Duna, Leslie Hogben +4
The distance matrix of a graph is the matrix containing the pairwise distances between vertices, and the distance Laplacian matrix is $\mathcal{D}^L(G)=T(G)-\m…
The zero forcing polynomial of a graph
Kirk Boyer, Boris Brimkov, Sean English +5
Zero forcing is an iterative graph coloring process, where given a set of initially colored vertices, a colored vertex with a single uncolored neighbor causes that neighbor to beco…
Throttling for the game of Cops and Robbers on graphs
Jane Breen, Boris Brimkov, Joshua Carlson +3
We consider the cop-throttling number of a graph for the game of Cops and Robbers, which is defined to be the minimum of , where is the number of co…
Applications of analysis to the determination of the minimum number of distinct eigenvalues of a graph
Beth Bjorkman, Leslie Hogben, Scarlitte Ponce +2
We establish new bounds on the minimum number of distinct eigenvalues among real symmetric matrices with nonzero off-diagonal pattern described by the edges of a graph and apply th…