A matrix sequence \(\{\Gamma (A^m)\}^\infty_{m=1}\) might converge even if the matrix \(A\) is not primitive

DOI10.1016/j.laa.2012.10.012zbMath1258.05015OpenAlexW2205287486MaRDI QIDQ1938687

Woongbae Park, Suh-Ryung Kim, Boram Park

Publication date: 22 February 2013

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2012.10.012

zbMATH Keywords

competition graphgraph sequenceirreducible Boolean (0,1)-matrixpowers of Boolean (0,1)-matricespowers of digraphs

Mathematics Subject Classification ID

Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Boolean and Hadamard matrices (15B34)

Related Items (2)

On the limit of the sequence \(\{ C^m ( D ) \}_{m = 1}^\infty\) for a multipartite tournament \(D\) ⋮ On the matrix sequence \(\{\Gamma(A^m)\}_{m=1}^\infty\) for a Boolean matrix \(A\) whose digraph is linearly connected

Cites Work

• A complete characterization of paths that are \(m\)-step competition graphs
• Inverting graphs of rectangular matrices
• Note on the \(m\)-step competition numbers of paths and cycles
• The competition-common enemy graph of a digraph
• The \(m\)-step competition graph of a digraph
• Connected triangle-free \(m\)-step competition graphs
• The \(m\)-step competition graphs of doubly partial orders
• The \(m\)-step, same-step, and any-step competition graphs
• COMPETITION INDICES OF STRONGLY CONNECTED DIGRAPHS
• COMPETITION INDICES OF TOURNAMENTS
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