Journal or Book Title
Electronic Journal of Linear Algebra
Zero forcing is a coloring game played on a graph where each vertex is initially colored blue or white and the goal is to color all the vertices blue by repeated use of a (deterministic) color change rule starting with as few blue vertices as possible. Probabilistic zero forcing yields a discrete dynamical system governed by a Markov chain. Since in a connected graph any one vertex can eventually color the entire graph blue using probabilistic zero forcing, the expected time to do this is studied. Given a Markov transition matrix for a probabilistic zero forcing process, an exact formula is established for expected propagation time. Markov chains are applied to determine bounds on expected propagation time for various families of graphs.
Chan, Yu; Curl, Emelie; Geneson, Jesse; Hogben, Leslie; Liu, Kevin; Odegard, Issac; and Ross, Michael S., "Using Markov Chains to Determine Expected Propagation Time for Probabilistic Zero Forcing" (2020). Mathematics Publications. 228.