  Let each vertex of a graph G = (V(G), E(G)) be given one of two colors, say,
"black" and "white". Let Z denote the (initial) set of black vertices of G. The
color-change rule converts the color of a vertex from white to black if the
white vertex is the only white neighbor of a black vertex. The set Z is said to
be a zero forcing set of G if all vertices of G will be turned black after
finitely many applications of the color-change rule. The zero forcing number of
G is the minimum of |Z| over all zero forcing sets Z \subseteq V (G). Zero
forcing parameters have been studied and applied to the minimum rank problem
for graphs in numerous articles. We define the iteration index of a zero
forcing set of a graph G to be the number of (global) applications of the
color-change rule required to turn all vertices of G black; this leads to a new
graph invariant, the iteration index of G - it is the minimum of iteration
indices of all minimum zero forcing sets of G. We present some basic properties
of the iteration index and discuss some preliminary results on certain graphs.
