Symmetry Parameters of Praeger-Xu Graphs
Praeger-Xu graphs are connected, symmetric, 4-regular graphs that are unusual both in that their automorphism groups are large, and in that vertex stabilizer subgroups are also large. Determining number and distinguishing number are parameters that measure the symmetry of a graph by investigating ad...
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| Main Authors | , |
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| Format | Journal Article |
| Language | English |
| Published |
20.09.2023
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| Subjects | |
| Online Access | Get full text |
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| Abstract | Praeger-Xu graphs are connected, symmetric, 4-regular graphs that are unusual
both in that their automorphism groups are large, and in that vertex stabilizer
subgroups are also large. Determining number and distinguishing number are
parameters that measure the symmetry of a graph by investigating additional
conditions that can be imposed on a graph to eliminate its nontrivial
automorphisms. In this paper, we compute the values of these parameters for
Praeger-Xu graphs. Most Praeger-Xu graphs are 2-distinguishable; for these
graphs we also provide the cost of 2-distinguishing. |
|---|---|
| AbstractList | Praeger-Xu graphs are connected, symmetric, 4-regular graphs that are unusual
both in that their automorphism groups are large, and in that vertex stabilizer
subgroups are also large. Determining number and distinguishing number are
parameters that measure the symmetry of a graph by investigating additional
conditions that can be imposed on a graph to eliminate its nontrivial
automorphisms. In this paper, we compute the values of these parameters for
Praeger-Xu graphs. Most Praeger-Xu graphs are 2-distinguishable; for these
graphs we also provide the cost of 2-distinguishing. |
| Author | Klivans, Max Cockburn, Sally |
| Author_xml | – sequence: 1 givenname: Sally surname: Cockburn fullname: Cockburn, Sally – sequence: 2 givenname: Max surname: Klivans fullname: Klivans, Max |
| BackLink | https://doi.org/10.48550/arXiv.2309.11474$$DView paper in arXiv |
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| Snippet | Praeger-Xu graphs are connected, symmetric, 4-regular graphs that are unusual
both in that their automorphism groups are large, and in that vertex stabilizer... |
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| SubjectTerms | Mathematics - Combinatorics |
| Title | Symmetry Parameters of Praeger-Xu Graphs |
| URI | https://arxiv.org/abs/2309.11474 |
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