The Q1-matrix completion problem

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.

The Q0-matrix completion problem

“…Most of the graph-theoretic terms used in this article can be found in any standard book, for example [1,6]. However for the convenience of the readers' of this article, we request them to follow the introduction part of the article [11][12][13].…”

The non-negative $Q_1$-matrix completion problem

“…A number of researchers studied matrix completion problems for different classes of matrices ( [5][6][7][8][9][10][11][12][13]). In 2009, DeAlba et al [2] solved the Q-matrix completion problem.…”