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Keywords:
Boolean matrix; index of convergence; digraph
Boolean matrix; index of convergence; digraph
Summary:
We obtain upper bounds for generalized indices of matrices in the class of nearly reducible Boolean matrices and in the class of critically reducible Boolean matrices, and prove that these bounds are the best possible.
References:
[1] Š. Schwarz: On the semigroup of binary relations on a finite set. Czechoslovak Math. J. 20(95) (1970), 632–679. MR 0296190 | Zbl 0228.20034
[2] R. A. Brualdi and B. Liu: Generalized exponents of primitive directed graphs. J. Graph Theory 14 (1990), 483–499. DOI 10.1002/jgt.3190140413 | MR 1067244
[3] B. Liu, B. Zhou, Q. Li and J. Shen: Generalized index of Boolean matrices. Ars Combin. 57 (2000), 257–255. MR 1796645
[4] E. A. Bender and T. W. Tucker: The exponents of strongly connected graphs. Canad. J. Math. 21 (1969), 769–782. DOI 10.4153/CJM-1969-088-3 | MR 0245458
[5] B. Liu: Generalized exponents of primitive, nearly reducible matrices. Ars Combin. 51 (1999), 229–239. MR 1675173 | Zbl 0977.05083
[6] Z. Jiang and J. Shao: On the set of indices of convergence for reducible matrices. Linear Algebra Appl. 148 (1991), 265–278. MR 1090764
[7] J. Shao and Q. Li: The index set for the class of irreducible Boolean matrices with given period. Linear and Multilinear Algebra 22 (1988), 285–303. DOI 10.1080/03081088808817840 | MR 0937171
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