Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distance-balanced closure of some graphs   In this paper we prove that any distance-balanced graph $G$ with
$\Delta(G)\geq |V(G)|-3$ is regular. Also we define notion of distance-balanced
closure of a graph and we find distance-balanced closures of trees $T$ with
$\Delta(T)\geq |V(T)|-3$.

13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn