An r-fold analogue of the positive semidefinite zero forcing process that
is carried out on the r-blowup of a graph is introduced and used to define
the fractional positive semidefinite forcing number. Properties of the graph
blowup when colored with a fractional positive semidefinite forcing set are
examined and used to define a three-color forcing game that directly computes
the fractional positive semidefinite forcing number of a graph. We develop a
fractional parameter based on the standard zero forcing process and it is shown
that this parameter is exactly the skew zero forcing number with a three-color
approach. This approach and an algorithm are used to characterize graphs whose
skew zero forcing number equals zero.Comment: 24 page
