### Abstract:

A partial matrix is a matrix with some entries speciﬁed while the other unspeciﬁed entries
are free to be chosen. Completion of partial matrix is a speciﬁc choice of unspeciﬁed
entries such that the resulting matrix satisﬁes a certain property. This study considers
nonnegative P
0
-matrix completion. The nonnegative P
- matrix completion problem determines
patterns of positions with the property that any partial nonnegative P
0
-matrix
that speciﬁes the pattern can be completed to a nonnegative P
-matrix. In particular the
study focusses on real 5x5 partial nonnegative P
0
0
-matrices specifying digraphs for p =
5 and q = 3, where p is the number of vertices and q is the number of arcs. The study
establishes that all digraphs for p = 5, q = 3 which are either cycles or acyclic digraphs
have zero completion to nonnegative P
0
-completion.
0