PRIMES: Zero Forcing in Graphs and its Applications

This award supports a partnership between Winston-Salem State University (WSSU) and the American Institute of Mathematics (AIM). WSSU is a historically black university (HBCU) that serves approximately 4400 undergraduate students. This award allows the PI to engage in a period of intensive research in graph theory, involving multiple activities at the American Institute of Mathematics (AIM), while also supporting efforts to increase participation in undergraduate research at WSSU and other institutions. This project’s research aims are focused on zero forcing, its variants, and their applications to graph searching and the inverse eigenvalue problem for graphs (IEPG). Zero forcing is an iterative graph coloring process that seeks to color all vertices of a graph in finite time from an initial set, where the vertices are colored according to a color change rule defined by the variant. There are numerous applications, including quantum control, network monitoring, and linear algebra. The PI will organize a small group of researchers to investigate these relationships for a number of zero forcing variants and their broader applications in research. Reconfiguration studies whether one solution to a problem can be obtained from another by a series of intermediate solutions, and this project will also study reconfiguration of various parameters related to zero forcing. The additional focus on research will also allow the PI to expand his research into the application of new tools available to investigate the IEPG more broadly. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.