Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $v$-number and Castelnuovo-Mumford regularity of graphs   We prove that for every integer $k\geq 1$, there exists a connected graph
$H_k$ such that $v(H_k)=reg(H_k)+k$, where $v(G)$ and $reg(G)$ denote the
$v$-number and the (Castelnuovo-Mumford) regularity of a graph $G$
respectively.

27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat