5 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…
Atoms in the Semigroup of Non-Negative Integer Matrices
Lindsay Dever, Eva G. Goedhart, Gregory S. Heilbrunn +1
In the semigroup , two-by-two matrices with non-negative integer entries and non-zero determinant, we study the factorization of matrices into atoms, or…
The Inverse Symplectic Eigenvalue Problem of a Graph
Himanshu Gupta, Leslie Hogben, Bryan Shader +1
Symplectic geometry plays an increasingly important role in mathematics, physics and applications, and naturally gives rise to interesting matrix families and properties. One of th…
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…
Building matrices with prescribed size and number of invertible submatrices
Edward S. T. Fan, Tony W. H. Wong
Given an ordered triple of positive integers , where , does there exist a matrix of size with exactly invertible submatrices of si…