Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The distinguishing number and the distinguishing index of line and
  graphoidal graphs   The distinguishing number (index) $D(G)$ ($D'(G)$) of a graph $G$ is the
least integer $d$ such that $G$ has an vertex labeling (edge labeling) with $d$
labels that is preserved only by a trivial automorphism. A graphoidal cover of
$G$ is a collection $\psi$ of (not necessarily open) paths in $G$ such that
every path in $\psi$ has at least two vertices, every vertex of $G$ is an
internal vertex of at most one path in $\psi$ and every edge of $G$ is in
exactly one path in $\psi$. Let $\Omega(G,\psi)$ denote the intersection graph
of $\psi$. A graph $H$ is called a graphoidal graph, if there exists a graph
$G$ and a graphoidal cover $\psi$ of $G$ such that $H\cong \Omega (G, \psi)$.
In this paper, we study the distinguishing number and the distinguishing index
of the line graph and the graphoidal graph of a simple connected graph $G$.

12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph