Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the distance domination number of bipartite graphs   A subset $D\subseteq V(G)$ is called a $k$-distance dominating set of $G$ if
every vertex in $V(G)\setminus D$ is within distance $k$ from some vertex of
$D$. The minimum cardinality among all $k$-distance dominating sets of $G$ is
called the $k$-distance domination number of $G$. In this note we give upper
bound on the $k$-distance domination number of a connected bipartite graph and
improve some results have been given like Theorem 2.1 and 2,7 in [Tian and Xu,
A note on distance domination of graphs, Australian Journal of Combinatorics,
43 (2009), 181-190].

8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
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
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas