4. Consider the following directed graph. [20] 9 F 10 4 4 7 8 3 S B E 2 6 2 3 5 7 C D T 11 12 (a) Find the shortest path from S to all other nodes using Dijkstra's algorithm. Show detailed computation of your answer. (15 points) (b) Given an undirected graph, how can you determine that the given graph also satisfies the condition of a Tree. Justify your answer with a suitable example. (5 points)