  Let R = K[x1,...,xr] be a polynomial ring over a field K. Let G be a graph
with vertex set {1,...,r} and let J be the cover ideal of G. We give a sharp
bound for the stability index of symbolic depth function sdstab(J). In the case
G is bipartite, it yields a sharp bound for the stability index of depth
function dstab(J) and this bound is exact if G is a forest.
