Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Divisibility graph for symmetric and alternating groups   Let $X$ be a non-empty set of positive integers and $X^*=X\setminus \{1\}$.
The divisibility graph $D(X)$ has $X^*$ as the vertex set and there is an edge
connecting $a$ and $b$ with $a, b\in X^*$ whenever $a$ divides $b$ or $b$
divides $a$. Let $X=cs~{G}$ be the set of conjugacy class sizes of a group $G$.
In this case, we denote $D(cs~{G})$ by $D(G)$. In this paper we will find the
number of connected components of $D(G)$ where $G$ is the symmetric group $S_n$
or is the alternating group $A_n$.

12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph