On the matrix sequence \Γ(A^m)\_m=1^∞ for a Boolean matrix A whose digraph is linearly connected

2013/07/15 by Jihoon Choi, Choi, Jihoon, Suh-Ryung Kim +1
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.1307.3881

19 pages, 4 figures

arxiv created 2013/07/15 · openalex publication_date 2013/07/15 · arxiv updated 2013/07/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we extend the results given by Park \em et al. \citeppk by studying the convergence of the matrix sequence \Γ(A^m)\_m=1^∞ for a matrix A ∈ 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 \Γ(A^m)\_m=1^∞ 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 \Γ(A^m)\_m=1^∞ is a J block diagonal matrix. All of these results are derived by studying the m-step competition graph of the digraph of A.

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