7. Define the distance d(Unuj) between nodes v' and uj in G = (V,E) the length of a short- est path between them. Then the diameter of G is D(G) axev d(vi,vj), that is, the largest distance among all pairs of vertices in V. Last, the radius of G is R(G) = min ev maxuEv d(u, v), that is, the smallest of the longest paths originating from each node in the network. For nEN 0 describe how you would construct the following: = max (a) A connected graph Gi (Vi, Es) where D(GGi) n when V (b) A connected graph G2 V2, E2) where D(G2)-2R(G2)-2n when V2l2n Hint for (b): Consider the cases when n is even and odd separately 7. Define the distance d(Unuj) between nodes v' and uj in G = (V,E) the length of a short- est path between them. Then the diameter of G is D(G) axev d(vi,vj), that is, the largest distance among all pairs of vertices in V. Last, the radius of G is R(G) = min ev maxuEv d(u, v), that is, the smallest of the longest paths originating from each node in the network. For nEN 0 describe how you would construct the following: = max (a) A connected graph Gi (Vi, Es) where D(GGi) n when V (b) A connected graph G2 V2, E2) where D(G2)-2R(G2)-2n when V2l2n Hint for (b): Consider the cases when n is even and odd separately