Let
be an
square matrix with
nonnegative entries and let
denote the number of positive entries in
. We consider the adjacency
matrix
with a corresponding
digraph with
vertices.
corresponds
to the number of directed edges in the corresponding digraph. We consider conditions on
to make the sequence
monotonic. Monotonicity is
known for
(except for three
nonmonotonic cases) and
;
we extend this to
.
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