Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The distinguishing number (index) and the domination number of a graph   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 set $S$ of vertices
in $G$ is a dominating set of $G$ if every vertex of $V(G)\setminus S$ is
adjacent to some vertex in $S$. The minimum cardinality of a dominating set of
$G$ is the domination number of $G$ and denoted by $\gamma (G)$. In this paper,
we obtain some upper bounds for the distinguishing number and the
distinguishing index of a graph based on its domination number.

36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat