Properties of a $q$-analogue of zero forcing
Combinatorics
2018-09-21 v1
Abstract
Zero forcing is a combinatorial game played on a graph where the goal is to start with all vertices unfilled and to change them to filled at minimal cost. In the original variation of the game there were two options. Namely, to fill any one single vertex at the cost of a single token; or if any currently filled vertex has a unique non-filled neighbor, then the neighbor is filled for free. This paper investigates a -analogue of zero forcing which introduces a third option involving an oracle. Basic properties of this game are established including determining all graphs which have minimal cost or for all possible , and finding the zero forcing number for all trees when .
Keywords
Cite
@article{arxiv.1809.07640,
title = {Properties of a $q$-analogue of zero forcing},
author = {Steve Butler and Craig Erickson and Shaun Fallat and H. Tracy Hall and Brenda Kroschel and Jephian C. -H. Lin and Bryan Shader and Nathan Warnberg and Boting Yang},
journal= {arXiv preprint arXiv:1809.07640},
year = {2018}
}