Brushing Number and Zero-Forcing Number of Graphs and their Line Graphs
Combinatorics
2020-08-25 v1
Abstract
In this paper we compare the brushing number of a graph with the zero-forcing number of its line graph. We prove that the zero-forcing number of the line graph is an upper bound for the brushing number by constructing a brush configuration based on a zero-forcing set for the line graph. Using a similar construction, we also prove the conjecture that the zero-forcing number of a graph is no more than the zero-forcing number of its line graph; moreover we prove that the brushing number of a graph is no more than the brushing number of its line graph. All three bounds are shown to be tight.
Cite
@article{arxiv.1609.05854,
title = {Brushing Number and Zero-Forcing Number of Graphs and their Line Graphs},
author = {Aras Erzurumluoglu and David Pike and Karen Meagher},
journal= {arXiv preprint arXiv:1609.05854},
year = {2020}
}
Comments
15 pages