The Q1-matrix completion problem

Kalyan Sinha

doi:10.26637/MJM0602/0023

Abstract

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.

Keywords:

Partial matrix, Matrix completion, Q1-matrix, Q1-completion, Digraph

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Kalyan Sinha Department of Mathematics, PSTDS Vidyapith, Chinsurah, Hooghly, West Bengal-712305, India. https://orcid.org/0000-0002-8491-6168

Pages: 443-450
Date Published: 01-04-2018
Vol. 6 No. 02 (2018): Malaya Journal of Matematik (MJM)

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