Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-cyclic graphs of (non)orientable genus one   Let $G$ be a finite non-cyclic group. The non-cyclic graph $\Gamma_G$ of $G$
is the graph whose vertex set is $G\setminus Cyc(G)$, two distinct vertices
being adjacent if they do not generate a cyclic subgroup, where $Cyc(G)=\{a\in
G: \langle a,b\rangle\ \text{is cyclic for each } b\in G\}$. In this paper, we
classify all finite non-cyclic groups $G$ such that $\Gamma_G$ has
(non)orientable genus one.

16
The categories of this paper are: stat
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
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The categories of this paper are: eess
12
The categories of this paper are: nucl-th