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::: Prim's Method

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Prim's Method

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Prim's Method

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Prim's Method
Question  1:  Find a minimal spanning tree for the connected weighted graph using  Prim's Method
Ans. (i) Prim's Method

Step - 1: Choose a vertex a and then select one of three edges incident with a with minimum weight.
W(ab) = 5
W(af) = 3
W(ae) = 5

So select af.

Step - 2: now we can choose minimum from the following edges.
W(ab) = 5
W(ae) = 5
W(fd) = 5
W(fb) = 6
Select ae.


Step - 3: now we can choose minimum from the following edges incidence on a or e or f.
W(ab) = 5
W(ed) = 7
W(fd) = 8
W(fb) = 6
Select ab.

Step - 4: now we can choose minimum from the following edges incidence on b or e or f.
W(bc) = 4
W(ed) = 7
W(fd) = 8
We have not included edge bf as it makes a cyclic loop as a-f-b
So, select bc.

Step - 4: now we can choose minimum from the following edges incidence on c or e or f.
W(cd) = 9
W(ed) = 7
W(fd) = 8

So, select ed.

Now all the vertices are traversed and this completes the formation of Minimal Spanning Tree.
Total Wt = w (bc + ab + af = ae + ed)
= 5 + 4 + 3 + 5 + 7 = 24

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