Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cycles in enhanced hypercubes   The enhanced hypercube $Q_{n,k}$ is a variant of the hypercube $Q_n$. We
investigate all the lengths of cycles that an edge of the enhanced hypercube
lies on. It is proved that every edge of $Q_{n,k}$ lies on a cycle of every
even length from $4$ to $2^n$; if $k$ is even, every edge of $Q_{n,k}$ also
lies on a cycle of every odd length from $k+3$ to $2^n-1$, and some special
edges lie on a shortest odd cycle of length $k+1$.

15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph