4 citations · 6 across the 2 of their papers we have counts for
6 papers
Restricted power domination and zero forcing problems
Chassidy Bozeman, Boris Brimkov, Craig Erickson +3
Power domination in graphs arises from the problem of monitoring an electric power system by placing as few measurement devices in the system as possible. A power dominating set of…
The inverse eigenvalue problem of a graph: Multiplicities and minors
Wayne Barrett, Steve Butler, Shaun M. Fallat +5
The inverse eigenvalue problem of a given graph is to determine all possible spectra of real symmetric matrices whose off-diagonal entries are governed by the adjacencies in $G…
The relationship between -forcing and -power domination
Daniela Ferrero, Leslie Hogben, Franklin H. J. Kenter +1
Zero forcing and power domination are iterative processes on graphs where an initial set of vertices are observed, and additional vertices become observed based on some rules. In b…
Expected values of parameters associated with the minimum rank of a graph
Tracy Hall, Leslie Hogben, Ryan R. Martin +1
We investigate the expected value of various graph parameters associated with the minimum rank of a graph, including minimum rank/maximum nullity and related Colin de Verdière-type…
Multi-part Nordhaus-Gaddum type problems for tree-width, Colin de Verdière type parameters, and Hadwiger number
Leslie Hogben, Jephian C. -H. Lin, Michael Young
A traditional Nordhaus-Gaddum problem for a graph parameter is to find a (tight) upper or lower bound on the sum or product of and (where denotes…
Table of minimum ranks of graphs of order at most 7 and selected optimal matrices
Laura DeLoss, Jason Grout, Leslie Hogben +3
The minimum rank of a simple graph is defined to be the smallest possible rank over all symmetric real matrices whose th entry (for ) is nonzero whenever …