14 citations · 20 across the 9 of their papers we have counts for
6 papers · 1 filter
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…
Regular Graphs of Degree at most Four that Allow Two Distinct Eigenvalues
Wayne Barrett, Shaun Fallat, Veronika Furst +3
For an matrix , let be the number of distinct eigenvalues of . If is a connected graph on vertices, let be the set of all real sy…
Sparsity of Graphs that Allow Two Distinct Eigenvalues
Wayne Barrett, Shaun Fallat, Veronika Furst +5
The parameter of a graph is the minimum number of distinct eigenvalues over the family of symmetric matrices described by . It is shown that the minimum number of edg…
Tight Frame Graphs Arising as Line Graphs
Veronika Furst, Howard Grotts
Dual multiplicity graphs are those simple, undirected graphs that have a weighted Hermitian adjacency matrix with only two distinct eigenvalues. From the point of view of frame the…
Note on Nordhaus-Gaddum problems for power domination
Katherine F. Benson, Daniela Ferrero, Mary Flagg +3
The upper and lower Nordhaus-Gaddum bounds over all graphs for the power domination number follow from known bounds on the domination number and examples. In this note we improve t…
Power domination and zero forcing
Katherine F. Benson, Daniela Ferrero, Mary Flagg +4
The power domination number arises from the monitoring of electrical networks and its determination is an important problem. Upper bounds for power domination numbers can be obtain…