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⇱ Quiz about Minimum Spanning Tree (MST) Quiz

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Question 1

Let G be a weighted graph with edge weights greater than one and G'be the graph constructed by squaring the weights of edges in G. Let T and T' be the minimum spanning trees of G and G', respectively, with total weights t and t'. Which of the following statements is TRUE?

  • T' = T with total weight t' = t2

  • T' = T with total weight t' < t2

  • T' != T but total weight t' = t2

  • None of the above

Question 2

Consider a graph G=(V, E), where V = { v1,v2,…,v100 }, E={ (vi, vj) ∣ 1≤ i < j ≤ 100} and weight of the edge (vi, vj)  is ∣i–j∣. The weight of minimum spanning tree of G is ________.

  • 99

  • 100

  • 98

  • 101

Question 3

Let s and t be two vertices in a undirected graph G + (V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s ∈ X and t ∈ Y. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y The edge e must definitely belong to:

  • the minimum weighted spanning tree of G

  • the weighted shortest path from s to t

  • each path from s to t

  • the weighted longest path from s to t

Question 4

If Kruskal’s algorithm is used for finding a minimum spanning tree of a weighted graph G with n vertices and m edges and edge weights are already given in a sorted list, then, What will be the time complexity to compute the minimum cost spanning tree given that union and find operations take amortized O(1) ?
  • O(m logn)
  • O(n)
  • O(m)
  • O(n logm)

Question 5

G = (V, E) is an undirected simple graph in which each edge has a distinct weight, and e is a particular edge of G. Which of the following statements about the minimum spanning trees (MSTs) of G is/are TRUE

I. If e is the lightest edge of some cycle in G, 
 then every MST of G includes e
II. If e is the heaviest edge of some cycle in G, 
 then every MST of G excludes e

  • I only

  • II only

  • both I and II

  • neither I nor II

Question 6

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.

  • 6

  • 7

  • 8

  • 9

Question 7

Given the intervals [(1, 4), (3, 6), (5, 7), (8, 9)], what would be the output of calling a function that solves the Job Scheduling Algorithm?

  • [(1, 4), (5, 7), (8, 9)]

  •  [(1, 4), (3, 6), (8, 9)]

  •  [(1, 4), (3, 6)]

  •  [(1, 4), (3, 6), (5, 7)]

Question 8

Let G be 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 ________.

  • 1000

  • 995

  • 2000

  • 1995

Question 9

Let G be a connected undirected graph with n vertices and m edges. Which of the following statements is true regarding the minimum number of edges required to create a cycle in G?

  • The minimum number of edges required to create a cycle is n.

  • The minimum number of edges required to create a cycle is n - 1.

  • The minimum number of edges required to create a cycle is m - n + 1.

  • The minimum number of edges required to create a cycle is m - n + 2.

Question 10

Consider the following graph:

👁 Image
Graph

Which edges would be included in the minimum spanning tree using Prim's algorithm starting from vertex A?

Options: a)  b)  c)  d) 

  • AB, BD, DE, EF, FC

  • AC, CD, DE, EB, BF

  • AB, BD, DE, EC, CF

  • AC, CD, DE, EB, FE

There are 22 questions to complete.

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