Zero forcing and its variants (Spring 2020)

Zero forcing is defined in terms of a color change rule, where there is an initial set of vertices that are colored blue, with all other vertices in the graph colored white. On each step, if u is a blue vertex that has exactly one white neighbor v, then the color of v is changed to blue. Zero forcing has been applied to problems in linear algebra, quantum systems control, and graph searching. There are several variants of zero forcing with different color change rules, including positive semidefinite zero forcing, skew zero forcing, probabilistic zero forcing, and leaky zero forcing. We will investigate problems related to zero forcing and its variants, such as:

• What is the smallest set of initial blue vertices that can be used to color the whole graph?

• How long does it take to color the whole graph with a given set of initial blue vertices?

People:

• Samson Baker (undergrad)

• Jesse Geneson (PostDoc)

• Matt Rayman (undergrad)

• Carolyn Reinhart (Grad)

• Zizheng Yang (undergrad)

Pre-requisites:

• Experience with proofs (in courses or research projects)

• Experience with combinatorics (Math 304) is desirable, but not necessary

• Experience with programming (e.g. Python) is desirable, but not necessary