Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Forbidden subgraphs of power graphs   The undirected power graph (or simply power graph) of a group $G$, denoted by
$P(G)$, is a graph whose vertices are the elements of the group $G$, in which
two vertices $u$ and $v$ are connected by an edge between if and only if either
$u=v^i$ or $v=u^j$ for some $i$, $j$.
  A number of important graph classes, including perfect graphs, cographs,
chordal graphs, split graphs, and threshold graphs, can be defined either
structurally or in terms of forbidden induced subgraphs. We examine each of
these five classes and attempt to determine for which groups $G$ the power
graph $P(G)$ lies in the class under consideration. We give complete results in
the case of nilpotent groups, and partial results in greater generality. In
particular, the power graph is always perfect; and we determine completely the
groups whose power graph is a threshold or split graph (the answer is the same
for both classes). We give a number of open problems.

14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
1
The categories of this paper are: cs
18
The categories of this paper are: econ
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol