Zero forcing is a combinatorial game played on a graph where the goal is to start with all vertices unfilled and to change them to filled at minimal cost. In the original variation of the game there were two options. Namely, to fill any one single vertex at the cost of a single token; or if any currently filled vertex has a unique non-filled neighbor, then the neighbor is filled for free. This paper investigates a q-analogue of zero forcing which introduces a third option involving an oracle. Basic properties of this game are established including determining all graphs which have minimal cost 1 or 2 for all possible q, and finding the zero forcing number for all trees when \(q=1\).

零强制是在图形上进行的组合游戏，其目标是从所有顶点都未填充开始，然后以最小的成本将它们更改为填充。在游戏的原始版本中，有两种选择。即，以单个令牌为代价填充任何单个顶点；或者，如果任何当前填充的顶点具有唯一的未填充邻居，则该邻居将免费填充。本文研究了零强迫的q模拟，它引入了涉及预言的第三种选择。建立了该游戏的基本属性，包括确定所有可能的q具有最小成本1或2的所有图，以及在\（q = 1 \）时为所有树找到零强迫数。