What is minimum spanning tree, Mathematics

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What is minimum spanning tree? Determine a railway network of minimal cost for the cities in the following graph using Kruskal's algorithm.

Ans: Minimum spanning tree in a connected weighted graph is spanning tree which has the smallest possible sum of weights of its edges.

2247_What is minimum spanning tree.png

We collect the edges in sorted order like this:

1121_What is minimum spanning tree 1.png

Select the edges (B,C),(D,F),(A,G),(C,D),(C,E).

After that we have option we may choose only one of (A,B) and (A,D), as selection of both makes a circuit. Assume we choose (A,B).

Similarly we may choose just only one of (G,H) and (F,H).Assume we select (F,H).

We Comprise a spanning tree as:

1500_What is minimum spanning tree 2.png

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