# Zero forcing number, Grundy domination number, and their variants

## TL;DR

This paper explores the relationships between zero forcing numbers and Grundy domination numbers, establishing bounds and methods to compute these parameters, thereby linking domination and minimum rank problems in graph theory.

## Contribution

It introduces new bounds and computational methods connecting zero forcing and Grundy domination variants, bridging domination and minimum rank problems.

## Key findings

- Grundy domination parameters are bounded above by minimum rank parameters.
- A method to compute the L-Grundy domination number using the Grundy total domination number.
- Linear algebra bounds for the L-Grundy domination number.

## 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. We show that the Grundy domination type parameters are bounded above by the 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.