A variation of zero forcing: leaky forcing

Dr. Ryan Moruzzi Jr
Assistant Professor of Mathematics
California State University, East Bay

Zero forcing on a graph is an iterative graph coloring process where, starting with an initial set of blue vertices, we try to force other non-blue vertices blue according to a color change rule. The zero forcing number of a graph was first defined in 2008 by a AIM (American Institute of Mathematics) working group as a method of bounding the maximum nullity of a graph. Motivated by monitoring an electrical network, leaks are introduced into the graph hindering the ability of vertices to force. Though we lose the connection with the maximum nullity of a graph, leaks in a graph present interesting new avenues of research pertaining to the area of zero forcing. We will introduce the topic of leaky zero forcing and a new variation of leaky zero forcing: leaky positive semidefinite zero forcing.