Tight Bounds on the Probabilistic Zero Forcing on Hypercubes and Grids

Abstract

Zero forcing is a deterministic iterative graph colouring process in which vertices are coloured either blue or white, and in every round, any blue vertices that have a single white neighbour force these white vertices to become blue. Here we study probabilistic zero forcing, where blue vertices have a non-zero probability of forcing each white neighbour to become blue.In this paper we explore the propagation time for probabilistic zero forcing on hypercubes. This is a preliminary work. We are currently working on grids and some other families of graphs. Stay tuned.