Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Half-arc-transitive graphs of prime-cube order of small valencies   A graph is called {\em half-arc-transitive} if its full automorphism group
acts transitively on vertices and edges, but not on arcs. It is well known that
for any prime $p$ there is no tetravalent half-arc-transitive graph of order
$p$ or $p^2$. Xu~[Half-transitive graphs of prime-cube order, J. Algebraic
Combin. 1 (1992) 275-282] classified half-arc-transitive graphs of order $p^3$
and valency $4$. In this paper we classify half-arc-transitive graphs of order
$p^3$ and valency $6$ or $8$. In particular, the first known infinite family of
half-arc-transitive Cayley graphs on non-metacyclic $p$-groups is constructed.

1
The categories of this paper are: cs
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn