Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper bounds of orders of automorphism groups of leafless metric graphs   We prove a tropical analogue of the theorem of Hurwitz: a leafless metric
graph of genus $g \ge 2$ has at most $12$ automorphisms when $g = 2$; $2^g g!$
automorphisms when $g \ge 3$. These inequalities are optimal; for each genus,
we give all metric graphs which have the maximum numbers of automorphisms. The
proof is written in terms of graph theory.

12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex