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University of Auckland

Time: 16:00-17:00 (GMT+8), Wednesday May 08th, 2024

Location: Zoom

**Abstract:**
Let \(\Gamma\) be a finite connected graph and
let \(G\) be a vertex-transitive group of automorphisms of \(\Gamma\). The pair \((\Gamma, G)\) is locally-\(L\) if the group induced by the action of the stabiliser
\(G_v\) on the neighbourhood of a vertex \(v\) is permutation isomorphic to \(L\).~Using this language, a classical theorem of Tutte states that for locally-\(A_3\) and locally-\(S_3\) pairs, \(|G|\) grows linearly with \(|V(\Gamma)|\).

More generally, given a transitive permutation group \(L\), we are interested in determining the growth of \(|G|\) as a function of \(|V(\Gamma)|\) for locally-\(L\) pairs \((\Gamma, G)\).
We present new results on this topic and highlight an exciting connection with the study of eigenspaces of graphs over finite fields.

Host: 丁兆宸 Zhaochen Ding