Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the order of vertex-stabilisers in vertex-transitive graphs with
  local group $C_p\times C_p$ or $C_p \wr C_2$   Let $p$ be a prime and let $L$ be either the intransitive permutation group
$C_p\times C_p$ of degree $2p$ or the transitive permutation group $C_p \wr
C_2$ of degree $2p$. Let $\Gamma$ be a connected $G$-vertex-transitive and
$G$-edge-transitive graph and let $v$ be a vertex of $\Gamma$. We show that if
the permutation group induced by the vertex-stabiliser $G_v$ on the
neighbourhood $\Gamma(v)$ is isomorphic to $L$ then either $|V(\Gamma)|\geq
p|G_v|\log_p\left(|G_v|/2\right)$, or $|V(\Gamma)|$ is bounded by a constant
depending only on $p$, or $\Gamma$ is a very-well understood graph. This
generalises a few recent results.

20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol