# Question: Given a flow network G V E let f1 and f2 be functions

Given a flow network G = (V, E), let f1 and f2 be functions from V × V to R. The flow sum f1 + f2 is the function from V × V to R defined by (26.4) (fi + f2) (u, v) = f1 (u, v) + f2(u, v) for all u, v ¬ V. If f1 and f2 are flows in G, which of the three flow properties must the flow sum f1 + f2 satisfy, and which might it violate?

**View Solution:**## Answer to relevant Questions

Let f be a flow in a network, and let α be a real number. The scalar flow product, denoted α f, is a function from V × V to R defined by (αf)(u, v) = α • f (u, v). Prove that the flows in a network ...Let G = (V, E) be a bipartite graph with vertex partition V = L R, and let G' be its corresponding flow network. Give a good upper bound on the length of any augmenting path found in G' during the execution of ...Prove that any sorting network on n inputs has depth at least lg n.There are two types of professional wrestlers: "good guys" and "bad guys." Between any pair of professional wrestlers, there may or may not be a rivalry. Suppose we have n professional wrestlers and we have a list of r pairs ...Given a directed graph G = (V, E), explain how to create another graph G′ = (V, E′) such that (a) G′ has the same strongly connected components as G, (b) G′ has the same component graph as G, and ...Post your question