The $Z_q$-forcing number for some graph families
Combinatorics
2023-05-22 v1
Abstract
The zero forcing number was introduced as a combinatorial bound on the maximum nullity taken over the set of real symmetric matrices that respect the pattern of an underlying graph. The -forcing game is an analog to the standard zero forcing game which incorporates inertia restrictions on the set of matrices associated with a graph. This work proves an upper bound on the -forcing number for trees. Furthermore, we consider the -forcing number for caterpillar cycles on vertices. We focus on developing game theoretic proofs of upper and lower bounds.
Cite
@article{arxiv.2305.11748,
title = {The $Z_q$-forcing number for some graph families},
author = {Jorge Blanco and Stephanie Einstein and Caleb Hostetler and Jurgen Kritschgau and Daniel Ogbe},
journal= {arXiv preprint arXiv:2305.11748},
year = {2023}
}