8 citations · 9 across the 6 of their papers we have counts for
5 papers · 1 filter
Matroid adjoints and the minimum rank of zero-nonzero matrix patterns
Louis Deaett, Kevin Grace
The problem of finding the minimum rank of a matrix with a given zero-nonzero pattern has been generalized to a class of matroids associated to the pattern. The fundamental lower b…
Relationships between minimum rank problem parameters for cobipartite graphs
Louis Deaett, Derek Young
For a simple graph, the minimum rank problem is to determine the smallest rank among the symmetric matrices whose off-diagonal nonzero entries occur in positions corresponding to t…
The Spark of Symmetric Matrices Described by a Graph
Louis Deaett, Shaun Fallat, Veronika Furst +3
We investigate the sparsity of null vectors of real symmetric matrices whose off-diagonal pattern of zero and nonzero entries is described by the adjacencies of a graph. We use the…
Orthogonal representations of Steiner triple system incidence graphs
Louis Deaett, H. Tracy Hall
The Heawood graph is the point-block incidence graph of the Fano plane (the unique Steiner triple system of order 7). We show that the minimum semidefinite rank of this graph is 10…
The minimum rank problem for circulants
Louis Deaett, Seth A. Meyer
The minimum rank problem is to determine for a graph the smallest rank of a Hermitian (or real symmetric) matrix whose off-diagonal zero-nonzero pattern is that of the adjacenc…