Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity of Powers of Unicyclic Graphs   Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge
ideal. In this paper we prove that if $G$ is a unicyclic graph then for all $s
\geq 1$ the regularity of $I(G)^s$ is exactly $2s+\text{reg}(I(G))-2$. We also
characterize the unicyclic graphs with regularity $\nu(G)+1$ and $\nu(G)+2$,
where $\nu(G)$ denotes the induced matching number of $G$.

1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int