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Exampe answer:

5. Consider the following acyclic digraph. B 3 E (a) List the topological sort of the graph (For multiple choice, please follow the Alphabetical order). (5 points) (6) Using Prim's Algorithm to get the Minimum Spanning Tree , Start from S (5 points) (c) Draw the maximum network flow from Sto E. (5 points) (a) Tepelegical Sort : 1 3 2 4 6 Topological Ordening S B SA SAB 0 SIA BE SABIED SABIEDIC SIA BED CF Topological Sort: Soxt: SAMB* E > DCF 6 (b) B (A 3 1 2 (E 2 3 6 2 Prim?s Algorithm (Minimum Spanning Tree) :- Staut Node :S Step 1: 2 (S Step 2: 2 Step 3: 1 2 Step 4: | 2 2 4 (E E) Step5: 1. 2 T . E 6 Step 6: E 2 G F (c) Maximum Network Flow from Sto E :- NG 3 04 2 3 D) () . 6 02 Sowuce : S Sink: E Initial flow is o Choosing path from s to E Augmenting path Bottleneck Capacity SA BE 1 1/6 1/3 (1/1 0/2 0/1 Residual Capuity B7 E is 0 0/4 ./2 013 016 012 Explanation Please refer to solution in this step. Answer Bottleneck Capacity 1 Augmenting path SABE SCADE 1