Zero forcing and its applications
January 30 to February 3, 2017
American Institute of Mathematics,
San Jose, California
and Michael Young
This workshop will be devoted to the theory of
zero forcing and its applications. Zero forcing is a propagation on graphs
described by the following process. Consider a graph $G$ and color each of its
vertices blue or white. A blue vertex $v$ can force a white vertex $w$ to be blue
if $w$ is the only white vertex in the neighborhood of $v$. A zero forcing set
of $G$ is a set of vertices $S \subset V(G)$ such that if the vertices of $S$ are
colored blue and the remaining vertices are colored white, then every vertex can
eventually become blue, after a repeated application of the forcing process. The
zero forcing number of $G, Z(G),$ is the minimum cardinality of a zero forcing
The concept of zero forcing has been used in multiple branches of science and
mathematics for many years. This workshop will discuss and study the zero
forcing number of graphs, and its applications to linear algebra, computer
science, power networks, and mathematical physics.
We will also look at the contemporary problems in computing zero forcing numbers
and the propagation time of zero forcing. Other types of zero forcing (e.g.
positive semidefinite zero forcing) have been defined and each type has been
defined on graphs, directed graphs, and graphs with loops. These related
parameters may be investigated also.
The main topics for the workshop are:
- Applications of zero forcing to inverse eigenvalue problems, PMU placement
problems, and quantum control problems.
- Connections to graph searching and certain minor-monotone parameters.
- Computational methods of zero forcing.
- Propagation times of zero forcing.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.
Papers arising from the workshop:
Rigid linkages and partial zero forcing
by Daniela Ferrero, Mary Flagg, H. Tracy Hall, Leslie Hogben, Jephian C.-H. Lin, Seth Meyer, Shahla Nasserasr, and Bryan Shader
Properties of a q-analogue of zero forcing
by Steve Butler, Craig Erickson, Shaun Fallat, H. Tracy Hall, Brenda Kroschel, Jephian C.-H. Lin, Bryan Shader, Nathan Warnberg, and Boting Yang
Restricted power domination and zero forcing problems
by Chassidy Bozeman, Boris Brimkov, Craig Erickson, Daniela Ferrero, Mary Flagg, and Leslie Hogben
Throttling for the game of Cops and Robbers on graphs
by Jane Breen, Boris Brimkov, Joshua Carlson, Leslie Hogben, K. E. Perry, and Carolyn Reinhart
Throttling positive semidefinite zero forcing propagation time on graphs
by Joshua Carlson, Leslie Hogben, Jurgen Kritschgau, Kate Lorenzen, Michael S. Ross, Seth Selken, and Vicente Valle Martinez
Families of graphs with maximum nullity equal to zero-forcing number
by J.S. Alameda, E. Curl, A. Grez, L. Hogben, O-N. Kingston, A. Schulte, D. Young, and M. Young, Spec. Matrices 6 (2018), 56–67 MR3760976