The Classification of Graphs on $8$ vertices with Coinciding Zero Forcing number and Maximum Nullity
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915339571298304 |
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| author | Barrett, Wayne Hunnell, Mark Hutchens, John Sinkovic, John |
| author_facet | Barrett, Wayne Hunnell, Mark Hutchens, John Sinkovic, John |
| contents | We study the minimum rank of a (simple, undirected) graph, which is the minimum rank among all matrices in a space determined by the graph. We determine the exact set of graphs on eight vertices for which the nullity of a minimum rank matrix does not coincide with a bound determined by the zero forcing number of a graph. Although our goal was to determine which eight-vertex graphs satisfy maximum nullity equal to the zero forcing number, we also established several additional methods to assist in the computation of minimum rank for general graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10726 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Classification of Graphs on $8$ vertices with Coinciding Zero Forcing number and Maximum Nullity Barrett, Wayne Hunnell, Mark Hutchens, John Sinkovic, John Combinatorics 05C50 We study the minimum rank of a (simple, undirected) graph, which is the minimum rank among all matrices in a space determined by the graph. We determine the exact set of graphs on eight vertices for which the nullity of a minimum rank matrix does not coincide with a bound determined by the zero forcing number of a graph. Although our goal was to determine which eight-vertex graphs satisfy maximum nullity equal to the zero forcing number, we also established several additional methods to assist in the computation of minimum rank for general graphs. |
| title | The Classification of Graphs on $8$ vertices with Coinciding Zero Forcing number and Maximum Nullity |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2506.10726 |