Zero Forcing Numbers and Path Cover Numbers

‎The zero forcing number‎, ‎Z(G) is a graph parameter that arise from a type of graph coloring‎. ‎It is an upper bound on the minimum number of induced paths P(G) in the graph‎. ‎We present families of graphs for which the zero forcing number and the path cover number are the same‎. ‎Also we show that for the vertex-sum $G \underset{v}{+} H$ of two graphs G and H which the zero forcing number and the path cover number are the same‎, ‎we have $Z(G \underset{v}{+} H) = P( G \underset{v}{+} H)$‎