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

DOI10.1016/j.laa.2014.02.046zbMath1286.05055arXiv1307.3881OpenAlexW2086338817WikidataQ112882253 ScholiaQ112882253MaRDI QIDQ2448228

Suh-Ryung Kim, Jihoon Choi

Publication date: 30 April 2014

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

Full work available at URL: https://arxiv.org/abs/1307.3881

zbMATH Keywords

graph sequenceindex of imprimitivitypowers of digraphs\(m\)-step competition graphsirreducible Boolean \((0, 1)\)-matriceslinearly connected digraphspowers of Boolean \((0, 1)\)-matrices

Mathematics Subject Classification ID

Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Directed graphs (digraphs), tournaments (05C20) Boolean and Hadamard matrices (15B34)

Cites Work

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• 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 \(m\)-step competition graph of a digraph
• Connected triangle-free \(m\)-step competition graphs
• A matrix sequence \(\{\Gamma (A^m)\}^\infty_{m=1}\) might converge even if the matrix \(A\) is not primitive
• 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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