Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zero forcing number, constrained matchings and strong structural
  controllability   The zero forcing number is a graph invariant introduced to study the minimum
rank of the graph. In 2008, Aazami proved the NP-hardness of computing the zero
forcing number of a simple undirected graph. We complete this NP-hardness
result by showing that the non-equivalent problem of computing the zero forcing
number of a directed graph allowing loops is also NP-hard. The rest of the
paper is devoted to the strong controllability of a networked system. This kind
of controllability takes into account only the structure of the interconnection
graph, but not the interconnection strengths along the edges. We provide a
necessary and sufficient condition in terms of zero forcing sets for the strong
controllability of a system whose underlying graph is a directed graph allowing
loops. Moreover, we explain how our result differs from a recent related result
discovered by Monshizadeh et al. Finally, we show how to solve the problem of
finding efficiently a minimum-size input set for the strong controllability of
a self-damped system with a tree-structure.

21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat