Question

Find the minimal spanning trees for the Graph below using Prim's algorithm. a) Starting from A. b) Starting from D, and c) Starting from E. What is the sum of the weighted value of the minimal path?

Answer 1

Using PRIM's Algorithm a) Starting from (A) Step 1:- let us consider, we pick a vertex "A and its adjacent edges are: W(A,B)=2 AR--- W(A,C) = 1 (min) 4 W(A,D)= 4 Step 2 - Now choose ending vertex of (A,C) iec W(CD = 2 Ar- -7 W (c, f) = 8 2 4 2 8 W (A,B) = 2 (min) i W(A,D=4 B ot W

Step 3 - Now choose ending verten of (A,B) ie, B W(B,0) = 3 W (C, D) = 2 (min) 21 & 2 WC, f) = 8 W(A, D = 4 3 3 of Step 4 - Now choose ending verten of (CD) ie, D 24 WCD,F) = 3 (min) WCD, E)=3 W(BD)=3 W (CE)=8 WCA,D)=4 i Step 5: Dow choose ending verten of (DA) ie F 12 WE,E) = 5 whe, E)=3 Emin) 7 21 W (B, D = 3 W (c,f) = 8 W(AID=4 --09 3 Since, total vertex are 6, we find five (5) Steps. So stop and final minimum spanning tree. Cost - ACTA B+ CD + DFT DE = 1 + 2 + 2 + 3 + 3 - 11 - - Solved -

D and its b starting from (D) Step 1 - Let us consider, we pick a verten adjacent edges are : A1 LE WCD,F)=3 WCD, E)=3 WCD, C) = 2(min) W(D,B) = 3 Step 2 - Now choose ending vertex of (DC) i.e, c. W(CA) = 1 (min A-1___ Wlc, f)=8 a y WCD,F) = 3 WCD, E)=3 WCD, B)=3 ko Step 3 - Now choose ending verten of (CA) ie, A. W(A,B) = 2 (min) AR- 2 - W(A ) = 4 wc, f) =8 W(DE)=3 W(D, E) = 3 W (0,B)=3 -200 Stepy - Now choose ending verten of (A,B) ie B.

DELIANO W(BD) = 3 WLAD = 4 WC, f=8 W(D,F) = 3 (min) WLD, E)=3 WID,B)=3 Step 5 Now choose ending vertex of (0€ le F. W(FE) = 5 AR- W(BD)=3 W CAO) = 4 w ce, f)=8 W(D,E) = 3 (min f Since, Total verten are 6, We find five (5) steps. So Stop and final minimum spanning tree. COSTA OC+ CA+AB+ DFT DE - 2 + 1 + 2 + 3 + 3 Solved

a vorten "t and its a) Starting from (E) Step 1 - Let us consides, we pick adjacent edges are;- W/ E, F) = 5 W(E, D)=3(min) Step2-Now choose endhing vertex of (ED) ies o WCD, C) = 2 (min) WCD, f) =3 W(D, B)=3 W(2,A)=4 WE,f) = 5 3 Stepp: How choose Euding verden of (19) le C. 2 W(e, f) =8 W(6A) = 1 (min) W(0,6)=3 W(D, B) =3 W(DAY W(6,F) = 5 B Step yo - Now chasse ending verten of Cc, A) LA..

12 W(A,B) = 2 (min) W(c, f)=8 Wlo,f=3 WED, B)= 3 W(BA) sy W(E,F) = 5 D 25 - Now. Choose ending verten of (A,B) ie, B WILD)=3 -- --- wc, f) 28 - WCD, f) = 3 (min) 1 WLD, A) =4 W(6,F) = 5 >F Since Total verten are 6, we find five (5 steps So Stop and final minimum spanning tree. COSTED + DC +CA+ AB+ DF - 3 +2 + 1 +2 + 3 之11Torved