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On the matrix sequence {Gamma(A^m)}_{m=1}^infinity for a Boolean matrix A whose digraph is linearly connected

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Authors

최지훈

Advisor
김서령
Major
사범대학 수학교육과
Issue Date
2014-08
Publisher
서울대학교 대학원
Keywords
irreducible boolean matrixlinearly connected digraphindex of imprimitivitym-step competition graph
Description
학위논문 (석사)-- 서울대학교 대학원 : 수학교육과, 2014. 8. 김서령.
Abstract
In this thesis, we extend the results given by Park et al. [12] by studying the convergence of the matrix sequence {Gamma(A^m)}_{m=1}^infinity for a matrix A in {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}^infinity 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}^infinity is a J block diagonal matrix. All of these results are derived by studying the m-step competition graph of the digraph of A.
Language
English
URI
https://hdl.handle.net/10371/127596
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College of Education (사범대학)Dept. of Mathematics Education (수학교육과)Theses (Master's Degree_수학교육과)
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