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SEMINAR: Groups and Combinatorics Seminar, Locally-transitive graphs and their vertex stabilisers

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Today's date is Thursday, March 04, 2021
Groups and Combinatorics Seminar, Locally-transitive graphs and their vertex stabilisers Other events...
Luke Morgan (UWA)

will speak on

Locally-transitive graphs and their vertex stabilisers

at 3pm Friday May the 9th in Weatherburn Lecture Theatre.

Abstract:

Let D be a graph with a group of automorphisms G and suppose that D is G-locally-arc-transitive (for each vertex x of D the vertex stabiliser G(x) acts transitively on the neighbourhood of x). Fixing the valency of D one can ask if there is a bound on the order of G(x)? For valency three there are fundamental results due to Tutte and Goldschmidt. We'll instead fix the `local actions, that is, the possible permutation groups induced on neighbourhoods in D (there can be at most two of these) and ask again: is there a bound on the order of G(x)? I will revisit some of the interesting results on this question. Then I will talk about some recent results like: when there can be a bound; when there is no bound; given a bound (and a little more) an instance when G(x) can be completely determined. Spread throughout this is joint work with Giudici, Giudici-Ivanov-Praeger and Spiga-Verret.
Speaker(s) Luke Morgan (UWA)
Location Weatherburn Lecture Theatre G.40
Contact Irene Pivotto <[email protected]>
Start Fri, 09 May 2014 15:00
End Fri, 09 May 2014 16:00
Submitted by Irene Pivotto <[email protected]>
Last Updated Fri, 09 May 2014 11:41
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