Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the monoid of partial isometries of a cycle graph   In this paper we consider the monoid $DPC_n$ of all partial isometries of a
$n$-cycle graph $C_n$. We show that $DPC_n$ is the submonoid of the monoid
$PORI_n$ of all oriented partial permutations on a $n$-chain whose elements are
precisely all restrictions of the dihedral group of order $2n$. For this
purpose, a useful characterization of an oriented transformation is established
first. Our main aims are to determine the rank and to exhibit a presentation of
$DPC_n$. We also describe Green's relations of $DPC_n$ and calculate its
cardinal.

15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga