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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 __________
Correct answer is '7'. Can you explain this answer?
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Let G be a complete undirected graph on 4 vertices, having 6 edges wit...
it is said maximum weight pssbl.
draw a triangle. 3 sides weight 1 2 3. and 4th point is in center. join it with tringle vertices.. got more 3 sides. new side weight 4 5 6. now draw mst. take 1 take 2. cant take 3, so take 4. 1+2+4=7
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Let G be a complete undirected graph on 4 vertices, having 6 edges wit...
Explanation:
A minimum weight spanning tree (MST) is a tree that spans all the vertices of a graph and has the lowest possible total edge weight. In a complete undirected graph on 4 vertices, the MST has only 3 edges.
To find the maximum possible weight that a minimum weight spanning tree of G can have, we need to consider the weights of the edges that are not included in the MST.
Let's assume that the MST has edges with weights w1, w2, and w3. Then, the other three edges have weights w4, w5, and w6.
To maximize the weight of the MST, we need to minimize the weights of the edges that are not included in the MST. Therefore, we need to include the edges with the smallest weights.
Let's consider two cases:
Case 1: The MST includes the edges with weights 1, 2, and 3.
In this case, the maximum possible weight of the MST is 1 + 2 + 3 = 6.
Case 2: The MST includes the edges with weights 1, 2, and 4 or 5.
In this case, the maximum possible weight of the MST is 1 + 2 + 4 (or 5) = 7.
Therefore, the maximum possible weight that a minimum weight spanning tree of G can have is 7.
A minimum weight spanning tree (MST) is a tree that spans all the vertices of a graph and has the lowest possible total edge weight. In a complete undirected graph on 4 vertices, the MST has only 3 edges.
To find the maximum possible weight that a minimum weight spanning tree of G can have, we need to consider the weights of the edges that are not included in the MST.
Let's assume that the MST has edges with weights w1, w2, and w3. Then, the other three edges have weights w4, w5, and w6.
To maximize the weight of the MST, we need to minimize the weights of the edges that are not included in the MST. Therefore, we need to include the edges with the smallest weights.
Let's consider two cases:
Case 1: The MST includes the edges with weights 1, 2, and 3.
In this case, the maximum possible weight of the MST is 1 + 2 + 3 = 6.
Case 2: The MST includes the edges with weights 1, 2, and 4 or 5.
In this case, the maximum possible weight of the MST is 1 + 2 + 4 (or 5) = 7.
Therefore, the maximum possible weight that a minimum weight spanning tree of G can have is 7.
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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 __________Correct answer is '7'. Can you explain this answer?
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