Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the orders of arc-transitive graphs   A graph is called {\em arc-transitive} (or {\em symmetric}) if its
automorphism group has a single orbit on ordered pairs of adjacent vertices,
and 2-arc-transitive its automorphism group has a single orbit on ordered paths
of length 2. In this paper we consider the orders of such graphs, for given
valency. We prove that for any given positive integer $k$, there exist only
finitely many connected 3-valent 2-arc-transitive graphs whose order is $kp$
for some prime $p$, and that if $d\ge 4$, then there exist only finitely many
connected $d$-valent 2-arc-transitive graphs whose order is $kp$ or $kp^2$ for
some prime $p$. We also prove that there are infinitely many (even) values of
$k$ for which there are only finitely many connected 3-valent symmetric graphs
of order $kp$ where $p$ is prime.

26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex