Question

For each graph, let s be the root. 1. Determine the minimum spanning tree of each graph using: a Prim's Algorithm b) Kruskal's Algorithm 2. Determine the shortest path tree of each graph using Dijkstra's Algorithm. 6 С (16 5 13 10 8 7 14 13 b 7 6 8 h 12 10 e

Answer 1

salution: = We know that in a minimum spanning toce Ivil = lvl TET TVI-1 here v' and E are the number of vertaxe and edges in the minimum spanning tree. (a) prim's algcaithan always select minimum cost edge connected & to the vertax, and never form cycle. 6 f 7 g 5. 6 to b 6 h d (6) Krus Kat's always select and algorithm: form cycle. น่าทาน cast adges never

S 3 7 9 s 7 7 b h d е. prish primis algorithya- - step-(1) . Step to 3 ů b sten-(3) oc -a 7 b 6 С step-4 g 5 7 6 e

f step-5 7 os 5 5 7 b e s 6 Step-(6) f 1 7 5 vo S 6. -step (7) f F 5 oo Z 5 g b 6 d Total cost= 6+7+5+ 7 + 7 +6 +5+9 52

Kruskal's algorithm :- Step-os Step-(2) 5.6 9 a a e - Step (3) ao 6 b. e G S Step-(4) C ☺ 5 6 f S Step-es) N a b b 6 d

6 Step-(6) СЕ y 3 a g 7 5 7 b h 6 total cost= 6+ 7+5+7+7+ 6 + 5ty 52. 6 Anste) co 9 16 9 5 10 a 13 13 of als PG 5 d 10 се е 12 vfG S v17 g 16 14 b17 516 d 13 23 e 22

(vertaal (Shortest path) d [v] » S 구 co b O 6. 17 16 22 13 14 17. e d a b С Le
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