Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the digraph of a unitary matrix   Given a matrix M of size n, a digraph D on n vertices is said to be the
digraph of M, when M_{ij} is different from 0 if and only if (v_{i},v_{j}) is
an arc of D. We give a necessary condition, called strong quadrangularity, for
a digraph to be the digraph of a unitary matrix. With the use of such a
condition, we show that a line digraph, LD, is the digraph of a unitary matrix
if and only if D is Eulerian. It follows that, if D is strongly connected and
LD is the digraph of a unitary matrix then LD is Hamiltonian. We conclude with
some elementary observations. Among the motivations of this paper are coined
quantum random walks, and, more generally, discrete quantum evolution on
digraphs.

21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol