Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distinguishing number and distinguishing index of graphs from primary
  subgraphs   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. Let $G$ be a connected
graph constructed from pairwise disjoint connected graphs $G_1,\ldots ,G_k$ by
selecting a vertex of $G_1$, a vertex of $G_2$, and identify these two
vertices. Then continue in this manner inductively. We say that $G$ is obtained
by point-attaching from $G_1, \ldots ,G_k$ and that $G_i$'s are the primary
subgraphs of $G$. In this paper, we consider some particular cases of these
graphs that are of importance in chemistry and study their distinguishing
number and index.

11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org