Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the matrix sequence $\{\Gamma(A^m)\}_{m=1}^\infty$ for a Boolean
  matrix $A$ whose digraph is linearly connected   In this paper, we extend the results given by Park {\em et al.} \cite{ppk} by
studying the convergence of the matrix sequence $\{\Gamma(A^m)\}_{m=1}^\infty$
for a matrix $A \in \mathcal{B}_n$ the digraph of which is linearly connected
with an arbitrary number of strong components. In the process for
generalization, we concretize ideas behind their arguments. We completely
characterize $A$ for which $\{\Gamma(A^m)\}_{m=1}^\infty$ converges. Then we
find its limit when all of the irreducible diagonal blocks are of order at
least two. We go further to characterize $A$ for which the limit of
$\{\Gamma(A^m)\}_{m=1}^\infty$ is a $J$ block diagonal matrix. All of these
results are derived by studying the $m$-step competition graph of the digraph
of $A$.

3
The categories of this paper are: physics
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an