6 papers
Sharp Nordhaus-Gaddum bounds for throttling
Ryan Blair, Gabriel Elvin, Veronika Furst +2
Throttling is a graph optimization problem, where the throttling number of a graph is the minimum sum or minimum product of the number of vertices in an initial set and the time re…
Transmission Zero Forcing
Adam H. Berliner, Chassidy Bozeman, Karen L. Collins +3
We initiate the study of transmission zero forcing, a variant of the well-studied zero forcing graph parameter. In this variant, a subset of vertices is assigned an initial unit we…
On the minimum number of distinct eigenvalues of triangle-free strongly regular graphs
Emily Egolf, Veronika Furst
Among the seven known (non-degenerate) triangle-free strongly regular graphs, we prove that the Clebsch graph describes a matrix with exactly two distinct eigenvalues while five of…
Sharp bounds for product and sum throttling numbers
Ryan Blair, Gabriel Elvin, Veronika Furst +3
Throttling in graphs optimizes a sum or product of resources used, such as the number of vertices in an initial set, and time required, such as the propagation time, to complete a…
Graphs with Bipartite Complement that Admit Two Distinct Eigenvalues
Wayne Barrett, Shaun Fallat, Veronika Furst +3
The parameter of an -vertex graph is the minimum number of distinct eigenvalues over the family of symmetric matrices described by . We show that all with $e(\…
Compatible Forts and Maximum Nullity of a Graph
Veronika Furst, John Hutchens, Lon Mitchell +1
We consider bounds on maximum nullity of a graph via transversal numbers of compatible collections of forts. Results include generalizations of theorems from symmetric to combinato…