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Let G be a complete undirected graph on 4 vertices, having 6 edges with weights being 1, 2, 3, 4, 5, and 6. The maximum possible weight that a minimum weight spanning tree of G can have is. 
  • a)
    6
  • b)
    7
  • c)
    8
  • d)
    9
Correct answer is option 'B'. Can you explain this answer?
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Let G be a complete undirected graph on 4 vertices, having 6 edges wit...
One graph that has maximum possible weight of spanning tree
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Let G be a complete undirected graph on 4 vertices, having 6 edges wit...
Explanation:

Understanding the Problem:
- We are given a complete undirected graph on 4 vertices, with 6 edges of different weights (1, 2, 3, 4, 5, and 6).
- We need to find the maximum possible weight that a minimum weight spanning tree of this graph can have.

Key Concepts:
- In a minimum weight spanning tree, we aim to connect all vertices with the minimum total weight possible.
- The minimum weight spanning tree of a graph connects all vertices with the minimum sum of edge weights while forming a tree.

Solution Approach:
- To find the maximum possible weight that a minimum weight spanning tree of the given graph can have, we need to consider the edges with the highest weights.
- Since the graph is complete, all vertices are connected to each other directly.
- The minimum weight spanning tree will include the edges with the lowest weights to connect all vertices without forming any cycles.

Calculating the Maximum Possible Weight:
- The minimum weight spanning tree of the given graph will have edges of weights 1, 2, 3, and 4 to connect all vertices without cycles.
- The maximum possible weight of this minimum weight spanning tree would be 1 + 2 + 3 + 4 = 10.
- However, since the maximum edge weight available is 6, the maximum weight that the minimum weight spanning tree can have is 1 + 2 + 3 = 6.
Therefore, the correct answer is option B) 7.
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