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# GATE | GATE-CS-2003 | Question 90

• Last Updated : 28 Jun, 2021

What is the weight of a minimum spanning tree of the following graph ?

(A) 29
(B) 31
(C) 38
(D) 41

Explanation: (a,c), (a,d), (d,b), (b,g), (g,h), (h,f), (h,i), (i,j), (i,e) = 31

Background required – Minimum Spanning Tree (Prims / Kruskal)

In these type of questions, always go for kruskalâ€™s algorithm to find out the the minimum spanning tree as it is easy and there are less chances of doing silly mistakes.

Algorithm:

Always pick the minimum edge weight and try to add to current forest (Collection of Trees) if no cycle is formed else discard.
As soon as u have added n-1 edges to the forest, stop and you have got your minimum spanning tree.

See the below image for construction of MST of this question.

Weight of minimum spanning tree = Sum of all the edges in Minimum Spanning tree
= 31

This explanation has been provided by Pranjul Ahuja.

http://www.ics.uci.edu/~eppstein/161/960206.html
https://en.wikipedia.org/wiki/Minimum_spanning_tree

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