Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.01872 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912360400158720 |
|---|---|
| author | Collier, Peter Janssen, Jeannette |
| author_facet | Collier, Peter Janssen, Jeannette |
| contents | Twisted hypercubes are graphs that generalize the structure of the hypercube by relaxing the symmetry constraint while maintaining degree-regularity and connectivity. We study the zero forcing number of twisted hypercubes. Zero forcing is a graph infection process in which a particular colour change rule is iteratively applied to the graph and an initial set of vertices. We use the alternative framing of forcing arc sets to construct a family of twisted hypercubes of dimension k$\geq 3$ with zero forcing sets of size $2^{k-1}-2^{k-3}+1$, which is below the minimum zero forcing number of the hypercube. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01872 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Zero Forcing Number of Twisted Hypercubes Collier, Peter Janssen, Jeannette Combinatorics Twisted hypercubes are graphs that generalize the structure of the hypercube by relaxing the symmetry constraint while maintaining degree-regularity and connectivity. We study the zero forcing number of twisted hypercubes. Zero forcing is a graph infection process in which a particular colour change rule is iteratively applied to the graph and an initial set of vertices. We use the alternative framing of forcing arc sets to construct a family of twisted hypercubes of dimension k$\geq 3$ with zero forcing sets of size $2^{k-1}-2^{k-3}+1$, which is below the minimum zero forcing number of the hypercube. |
| title | The Zero Forcing Number of Twisted Hypercubes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2505.01872 |