Zero blocking numbers of graphs with complexity results
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912552125988864 |
|---|---|
| author | Lin, Hau-Yi Lin, Wu-Hsiung Chang, Gerard Jennhwa |
| author_facet | Lin, Hau-Yi Lin, Wu-Hsiung Chang, Gerard Jennhwa |
| contents | For a graph $G$ in which vertices are either black or white, a zero forcing process is an iterative vertex color changing process such that the only white neighbor of a black vertex becomes black in the next time step. A zero forcing set is an initial subset of black vertices in a zero forcing process ultimately expands to include all vertices of the graph; otherwise we call its complement a zero blocking set. The zero blocking number $B(G)$ of $G$ is the minimum size of a zero blocking set. This paper determines zero blocking numbers of the union and the join of two graphs. It also determines all minimum zero blocking sets of hypercubes. Finally, a linear-time algorithm for the zero blocking numbers of trees is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17785 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Zero blocking numbers of graphs with complexity results Lin, Hau-Yi Lin, Wu-Hsiung Chang, Gerard Jennhwa Combinatorics 05C69, 05C85, 68R10 For a graph $G$ in which vertices are either black or white, a zero forcing process is an iterative vertex color changing process such that the only white neighbor of a black vertex becomes black in the next time step. A zero forcing set is an initial subset of black vertices in a zero forcing process ultimately expands to include all vertices of the graph; otherwise we call its complement a zero blocking set. The zero blocking number $B(G)$ of $G$ is the minimum size of a zero blocking set. This paper determines zero blocking numbers of the union and the join of two graphs. It also determines all minimum zero blocking sets of hypercubes. Finally, a linear-time algorithm for the zero blocking numbers of trees is given. |
| title | Zero blocking numbers of graphs with complexity results |
| topic | Combinatorics 05C69, 05C85, 68R10 |
| url | https://arxiv.org/abs/2508.17785 |