In question 300 edges given what does that statement say ? I didn't get it ?

33 votes

Let $G$ be a connected undirected graph of $100$ vertices and $300$ edges. The weight of a minimum spanning tree of $G$ is $500$. When the weight of each edge of $G$ is increased by five, the weight of a minimum spanning tree becomes ______.

55 votes

Best answer

4 votes

Since there are 100 vertices, there must be 99 edges in Minimum Spanning Tree (MST). When weight of every edge is increased by 5, the increment in weight of MST is = 99 * 5 = 495 So new weight of MST is 500 + 495 which is 995

0 votes

Adding or multiplying **all **the edges of an MST by a constant does not change the MST, it only changes the value of MST.

Vertices = 100.

Hence, edges in the MST = 99.

Weight = 500

Since the MST would remain the same; just the edge weights would be upgraded by 5, upgraded MST weight:

$500+99(5)=995$