Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perfect codes in Cayley graphs   Given a graph $\Gamma$, a subset $C$ of $V(\Gamma)$ is called a perfect code
in $\Gamma$ if every vertex of $\Gamma$ is at distance no more than one to
exactly one vertex in $C$, and a subset $C$ of $V(\Gamma)$ is called a total
perfect code in $\Gamma$ if every vertex of $\Gamma$ is adjacent to exactly one
vertex in $C$. In this paper we study perfect codes and total perfect codes in
Cayley graphs, with a focus on the following themes: when a subgroup of a given
group is a (total) perfect code in a Cayley graph of the group; and how to
construct new (total) perfect codes in a Cayley graph from known ones using
automorphisms of the underlying group. We prove several results around these
questions.

31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph