Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the $n-$dominating graph of specific graphs   Let $G=(V,E)$ be a graph. A set $S\subseteq V(G)$ is a dominating set, if
every vertex in $V(G)\backslash S$ is adjacent to at least one vertex in $S$.
The $k$-dominating graph of $G$, $D_k (G)$, is defined to be the graph whose
vertices correspond to the dominating sets of $G$ that have cardinality at most
$k$. Two vertices in $D_k(G)$ are adjacent if and only if the corresponding
dominating sets of $G$ differ by either adding or deleting a single vertex. In
this paper we consider and study the $n$-dominating graph of specific graphs.

18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph