Stabilizers of consistent walks
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914813004742656 |
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| author | Lekše, Maruša |
| author_facet | Lekše, Maruša |
| contents | A walk of length $n$ in a graph is consistent if there exists an automorphism of the graph that maps the initial $n-1$ vertices to the final $n-1$ vertices of the walk. In this paper we find some sufficient conditions for a consistent walk in an arc-transitive graph to have a trivial pointwise stabilizer. We show that in that case, the size of the smallest generating set of the group is bounded by the valence of the graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16691 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stabilizers of consistent walks Lekše, Maruša Combinatorics 05E18, 05C25 A walk of length $n$ in a graph is consistent if there exists an automorphism of the graph that maps the initial $n-1$ vertices to the final $n-1$ vertices of the walk. In this paper we find some sufficient conditions for a consistent walk in an arc-transitive graph to have a trivial pointwise stabilizer. We show that in that case, the size of the smallest generating set of the group is bounded by the valence of the graph. |
| title | Stabilizers of consistent walks |
| topic | Combinatorics 05E18, 05C25 |
| url | https://arxiv.org/abs/2405.16691 |