The Zero Forcing Polynomial of a Ladder Graph

Abstract

Zero forcing is a graph infection parameter which allows vertices of a graph to be colored using the color-change rule. Vertices of a graph are initially colored either blue or white. The color-change rule states that if a blue vertex has only one white neighbor then it can color its neighbor blue. A zero forcing set of a graph is a set of initially colored blue vertices such that all other vertices in the graph become blue when the color-change rule is applied. Zero forcing was first introduced in 2008 and has applications in quantum physics, computer science, power networks, and mathematical physics. The zero forcing polynomial of a graph counts the number of zero forcing sets of all possible sizes of a graph. Our research team is working to find a generalized formula for the zero forcing polynomial of a specific type of graph - the ladder graph.