Affiliation:
1. University of Primorska , UP FAMNIT, Glagoljaška 8; and University of Primorska, UP IAM, Muzejski trg 2, 6000 Koper , Slovenia
Abstract
Abstract
We consider a finite, connected and simple graph Γ that admits a vertex-transitive group of automorphisms 𝐺.
Under the assumption that, for all
x
∈
V
(
Γ
)
x\in V(\Gamma)
, the local action
G
x
Γ
(
x
)
G_{x}^{\Gamma(x)}
is the action of
Sym
(
n
)
\operatorname{Sym}(n)
on ordered pairs, we show that the group
G
x
[
3
]
G_{x}^{[3]}
, the point-wise stabiliser of a ball of radius three around 𝑥, is trivial.
Subject
Algebra and Number Theory