A complete, acyclic flow graph on n nodes 1,2,... , n has arcs i -» j for all nodes i and j such that i  a) For what values of n is this graph reducible?  b) Does your answer to (a) change if you add...

A complete, acyclic flow graph on n nodes 1,2,... , n has arcs i -» j for all nodes i and j such that i <>

a) For what values of n is this graph reducible?

b) Does your answer to (a) change if you add self-loops i -+ i for all nodes i?

The natural loop of a back edge n -+ h was defined to be h plus the set of nodes that can reach n without going through h. Show that h dominates all the nodes in the natural loop of n -+ h.