Consider the following network( the numbers are edge capacities)

(A 6 3 (a) Find the maximum flow f and a minimum cut. (b) Draw the residual graph Gr (along with its edge capacities). In this residual network, mark the vertices reachable from S and the vertices from which T is reachable. (c) An edge of a network is called a bottleneck edge if increasing its capacity results in an increase in the maximum flow. List all bottleneck edges in the above network which has no bottleneck edges. (Hint: Start by running the usual network flow algorithm, and then (d) Give a very simple example (containing at most four nodes) of a network (e) Give an efficient algorithm to identify all bottleneck edges in a network. examine the residual graph.)