5 papers
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…
Fault Tolerant Zero Forcing
Asher Brown, Mark Hunnell, Za'Kiyah Toomer-Sanders +1
Zero forcing is an iterative graph coloring process studied for its wide array of applications. In this process, the vertices of the graph are initially designated as blue or white…
Zero forcing propagation time intervals and graphs with fixed propagation time
Daniela Ferrero, H. Tracy Hall, Leslie Hogben +2
Zero forcing in a graph refers to the evolution of vertex states under repeated application of a color change rule. Typically the states are chosen to be blue and white, and a forc…
The Classification of Graphs on vertices with Coinciding Zero Forcing number and Maximum Nullity
Wayne Barrett, Mark Hunnell, John Hutchens +1
We study the minimum rank of a (simple, undirected) graph, which is the minimum rank among all matrices in a space determined by the graph. We determine the exact set of graphs on…
Reconfiguration of Minimum PSD Forcing Sets and Minimum Skew Forcing Sets
Novi Bong, Mary Flagg, Mark Hunnell +4
Reconfiguration graphs provide a way to represent relationships among solutions to a problem, and have been studied in many contexts. We investigate the reconfiguration graphs corr…