Mathematics Faculty Colloquium by Prof. Josh Carlson, Friday, September 27, 1 – 1:45 pm

Throttling for the Game of Cops and Robbers and PSD Zero Forcing by Prof. Josh Carlson, Mathematics Faculty Colloquium, Friday, September 27, 1 – 1:45 pm, Stetson Court Classroom 105

Abstract:  Cops and robbers is a game played on graphs in which a team of cops and a single robber move from vertex to vertex by traversing the edges of the graph. The cops win if at any time, a cop moves to the position of the robber. If it is impossible for the cops to guarantee capture of the robber, the robber wins the game. The idea of throttling is to optimize the balance between the number of cops and the time taken to capture the robber. This idea can also be applied to a process called zero forcing. Specifically, zero forcing is a process in graphs that uses a color change rule to force the vertices to become blue. In this context, the throttling number minimizes the sum of the number of blue vertices at the start of the process and time taken for all vertices to become blue. Recently, a variant called positive semidefinite (PSD) zero forcing has been connected to the game of cops and robbers. This talk will highlight this connection and present recent results on both topics.