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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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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International