Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the power graph of the direct product of two groups   The power graph $P(G)$ of a finite group $G$ is the graph with vertex set $G$
and two distinct vertices are adjacent if either of them is a power of the
other. Here we show that the power graph $P(G_1 \times G_2)$ of the direct
product of two groups $G_1$ and $G_2$ is not isomorphic to either of the
direct, cartesian and normal product of their power graphs $P(G_1)$ and
$P(G_2)$. A new product of graphs, namely generalized product, has been
introduced and we prove that the power graph $P(G_1 \times G_2)$ is isomorphic
to a generalized product of $P(G_1)$ and $P(G_2)$.

28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga