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The Q1-matrix completion problem

Kalyan Sinha

2018Malaya Journal of MatematikComputer Science被引 3开放获取

摘要

A matrix is a $Q_1$-matrix if it is a $Q$-matrix with positive diagonal entries. A digraph $D$ is said to have $Q_1$-completion if every partial $Q_1$-matrix specifying $D$ can be completed to a $Q_1$-matrix. In this paper, necessary and sufficient conditions for a digraph to have $Q_1$-completion are obtained. Later on the relationship among the completion problem of $Q_1$-matrix and some other class of matrices are discussed. Finally, the digraphs of order at most four that include all loops and have $Q_1$-completion are characterized.

引用本文（GB/T 7714）

DOI：https://doi.org/10.26637/mjm0602/0023