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- W1723975037 abstract "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 $A$." @default.
- W1723975037 created "2016-06-24" @default.
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- W1723975037 date "2013-07-15" @default.
- W1723975037 modified "2023-09-26" @default.
- W1723975037 title "On the matrix sequence ${Gamma(A^m)}_{m=1}^infty$ for a Boolean matrix $A$ whose digraph is linearly connected" @default.
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- W1723975037 doi "https://doi.org/10.48550/arxiv.1307.3881" @default.
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