Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cores of imprimitive symmetric graphs of order a product of two distinct
  primes   A retract of a graph $\Gamma$ is an induced subgraph $\Psi$ of $\Gamma$ such
that there exists a homomorphism from $\Gamma$ to $\Psi$ whose restriction to
$\Psi$ is the identity map. A graph is a core if it has no nontrivial retracts.
In general, the minimal retracts of a graph are cores and are unique up to
isomorphism; they are called the core of the graph. A graph $\Gamma$ is
$G$-symmetric if $G$ is a subgroup of the automorphism group of $\Gamma$ that
is transitive on the vertex set and also transitive on the set of ordered pairs
of adjacent vertices. If in addition the vertex set of $\Gamma$ admits a
nontrivial partition that is preserved by $G$, then $\Gamma$ is an imprimitive
$G$-symmetric graph. In this paper cores of imprimitive symmetric graphs
$\Gamma$ of order a product of two distinct primes are studied. In many cases
the core of $\Gamma$ is determined completely. In other cases it is proved that
either $\Gamma$ is a core or its core is isomorphic to one of two graphs, and
conditions on when each of these possibilities occurs is given.

34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph