# GATE2015-3-40

3.6k views
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 ______.

edited

First find no of edges in mst.
Mst has $n-1$ edges where $n$ is no of vertices. $100-1 =99$ edges
Each $99$ edges in mst increases by $5$ so weight in mst increased $99*5=495$
Now total weight of mst $=500+495=995$

edited
1
In question 300 edges given what does that statement say ? I didn't get it ?
4
The total number of edges present in a graph is 300.

But as we know that the minimum number of edges required in a minimal connected single component graph is n-1.
No of edges =99 , now mention condition 99*5 = 495+500 = 995
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

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:

$500+99(5)=995$

## Related questions

1
2.8k views
Suppose $c = \langle c, \dots, c[k-1]\rangle$ is an array of length $k$, where all the entries are from the set $\{0, 1\}$. For any positive integers $a \text{ and } n$, consider the following pseudocode. DOSOMETHING (c, a, n) $z \leftarrow 1$ ... , then the output of DOSOMETHING(c, a, n) is _______.
The graph shown below has $8$ edges with distinct integer edge weights. The minimum spanning tree (MST) is of weight $36$ and contains the edges: $\{(A, C), (B, C), (B, E), (E, F), (D, F)\}$. The edge weights of only those edges which are in the MST are given in the figure shown below. The minimum possible sum of weights of all $8$ edges of this graph is_______________.
Consider the relation $X(P,Q,R,S,T,U)$ with the following set of functional dependencies $F = \{ \\ \; \; \{P, R\} \rightarrow \{S, T\}, \\ \; \; \{P, S, U\} \rightarrow \{Q, R\} \\ \; \}$ Which of the following is the trivial functional dependency in $F^+$, where $F^+$ is closure ... $\{P, R\} \rightarrow \{R, T\}$ $\{P, S\} \rightarrow \{S\}$ $\{P, S, U\} \rightarrow \{Q\}$
While inserting the elements $71, 65, 84, 69, 67, 83$ in an empty binary search tree (BST) in the sequence shown, the element in the lowest level is $65$ $67$ $69$ $83$