Zero forcing number, Grundy domination number, and their variants

Abstract

This paper presents strong connections between four variants of the zero forcing number and four variants of the Grundy domination number. These connections bridge the domination problem and the minimum rank problem, providing a linear algebra approach to the domination problem. We show that several Grundy domination type parameters are bounded above by minimum rank type parameters. We also give a method to calculate the L-Grundy domination number by the Grundy total domination number, giving some linear algebra bounds for the L-Grundy domination number.