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Zero forcing is a process on graphs in which a color change rule is used toforce vertices to become blue. The amount of time taken for all vertices in thegraph to become blue is the propagation time. Throttling minimizes the sum ofthe number of initial blue vertices and the propagation time. In this paper, westudy throttling in the context of directed graphs (digraphs). We characterizeall simple digraphs with throttling number at most $t$ and examine the changein the throttling number after flipping arcs and deleting vertices. We alsointroduce the orientation throttling interval (OTI) of an undirected graph,which is the range of throttling numbers achieved by the orientations of thegraph. While the OTI is shown to vary among different graph families, somegeneral bounds are obtained. Additionally, the maximum value of the OTI of apath is conjectured to be achieved by the orientation of a path whose arcsalternate in direction. The throttling number of this orientation is exactlydetermined in terms of the number of vertices.

Throttling for standard zero forcing on directed graphs