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…