Let a, b and c be three vertices of a strongly connected multidigraph D=(V,A,ψ) such that ∣V∣≥4. For any two vertices u and v of D, we define the distance d(u,v) to be the smallest length of a path from u to v. (This definition is the obvious analogue of Definition 5.5.1 for digraphs.)
((a)) Prove that d(b,c)+d(c,a)+d(a,b)≤3∣V∣−4.
((b)) For each n≥5, construct an example in which ∣V∣=n and d(b,c)+d(c,a)+d(a,b)=3∣V∣−4. (No proof is required for the example.)