Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On two graph isomorphism problems   In 2015, Bogdanowicz gave a necessary and sufficient condition for a
4-regular circulant graph to be isomorphic to the Cartesian product of two
cycles. Accordion graphs, denoted by $A[n,k]$, are 4-regular graphs on two
parameters $n$ and $k$ which were recently introduced by the authors and
studied with regards to Hamiltonicity and matchings. These graphs can be
obtained by a slight modification in some of the edges of the Cartesian product
of two cycles. Motivated by the work of Bogdanowicz, the authors also
determined for which values of $n$ and $k$ the accordion graph $A[n,k]$ is
circulant. In this work we investigate what parameters a 4-regular circulant
graph must have in order to be isomorphic to an accordion graph, thus providing
a complete characterisation similar to that given by Bogdanowicz. We also give
a necessary and sufficient condition for two accordion graphs with distinct
parameters to be isomorphic.

13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an