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Vertex-primitive graphs having vertices with almost equal neighbourhoods, and vertex-primitive graphs of valency 5 Verret, Gabriel
Description
A graph is vertex-primitive if its automorphism group does not preserve any nontrivial partition of its vertex-set. It is an easy exercise to prove that (apart from some trivial exceptions) a vertex-primitive graph cannot have distinct vertices with equal neighbourhoods. I will discuss some results about vertex-primitive graphs having two vertices with “almost” equal neighbourhoods, and how these results were used to answer a question of Araújo and Cameron about synchronising permutation groups.
These results were also the motivation for a recent classification of vertex-primitive graphs of valency 5. (Graphs of valency at most 4 had previously been classified.) I will describe this classification, some of the issues that arose in the proof, and the connection with the previous problem.
Item Metadata
| Title |
Vertex-primitive graphs having vertices with almost equal neighbourhoods, and vertex-primitive graphs of valency 5
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2016-11-14T10:05
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| Description |
A graph is vertex-primitive if its automorphism group does not preserve any nontrivial partition of its vertex-set. It is an easy exercise to prove that (apart from some trivial exceptions) a vertex-primitive graph cannot have distinct vertices with equal neighbourhoods. I will discuss some results about vertex-primitive graphs having two vertices with “almost” equal neighbourhoods, and how these results were used to answer a question of Araújo and Cameron about synchronising permutation groups.
These results were also the motivation for a recent classification of vertex-primitive graphs of valency 5. (Graphs of valency at most 4 had previously been classified.) I will describe this classification, some of the issues that arose in the proof, and the connection with the previous problem.
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| Extent |
22 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: University of Western Australia
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| Series | |
| Date Available |
2017-05-15
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0347502
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| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
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| Scholarly Level |
Postdoctoral
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International