Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The maximal subgroups and the complexity of the flow semigroup of finite
  (di)graphs   The flow semigroup, introduced by John Rhodes, is an invariant for digraphs
and a complete invariant for graphs. After collecting together previous partial
results, we refine and prove Rhodes's conjecture on the structure of the
maximal groups in the flow semigroup for finite, antisymmetric, strongly
connected digraphs.
  Building on this result, we investigate and fully describe the structure and
actions of the maximal subgroups of the flow semigroup acting on all but $k$
points for all finite digraphs and graphs for all $k\geq 1$. A linear algorithm
(in the number of edges) is presented to determine these so-called `defect $k$
groups' for any finite (di)graph.
  Finally, we prove that the complexity of the flow semigroup of a 2-vertex
connected (and strongly connected di)graph with $n$ vertices is $n-2$,
completely confirming Rhodes's conjecture for such (di)graphs.

7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg