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.