7. Let G be an edge weighted graph whose SHORTEST PATH TREE T from VERTEX v₁ is: V9 V5 3 V1 5 2 V10 7 V6 4 V2 6 2 V11 V7 5 V3 V12 3 V8 V4 (The numbers on the edges are the weights of the edges of T.) Note that the above graph is the shortest path tree, NOT the graph G. Graph G has other edges and weights on those edges, but this information is NOT available. (a) Is it possible to determine a shortest path from v3 to v₁1? If so, give the path and its length. If not, explain why not. (b) Is it possible to determine a shortest path from v5 to v7? If so, give the path and its length. If not, explain why not.

7. Let G be an edge weighted graph whose SHORTEST PATH TREE T from VERTEX v₁ is: V9 V5 3 V1 5 2 V10 7 V6 4 V2 6 2 V11 V7 5 V3 V12 3 V8 V4 (The numbers on the edges are the weights of the edges of T.) Note that the above graph is the shortest path tree, NOT the graph G. Graph G has other edges and weights on those edges, but this information is NOT available. (a) Is it possible to determine a shortest path from v3 to v₁1? If so, give the path and its length. If not, explain why not. (b) Is it possible to determine a shortest path from v5 to v7? If so, give the path and its length. If not, explain why not.