  We consider a quantum walk with two marked vertices, sender and receiver, and
analyze its application to perfect state transfer on complete bipartite graphs.
First, the situation with both the sender and the receiver vertex in the same
part of the graph is considered. We show that in this case the dynamics of the
quantum walk is independent of the size of the second part and reduces to the
one for the star graph where perfect state transfer is achieved. Second, we
consider the situation where the sender and the receiver vertex are in the
opposite parts of the graph. In such a case the state transfer with unit
fidelity is achieved only when the parts have the same size.
