gs gs122 Minimum Spanning Tree - Minimum Spanning Tree - Quiz No.1

gs gs122 Data Communication and Computer Network Quiz

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Question 1: Which of the following is false in the case of a spanning tree of a graph G?

It is tree that spans G

It is a subgraph of the G

It includes every vertex of the G

It can be either cyclic or acyclic

Question 2: Every graph has only one minimum spanning tree.

True

False

Question 3: Consider a complete graph G with 4 vertices. The graph G has ____ spanning trees.

Question 4: The travelling salesman problem can be solved using _________

A spanning tree

A minimum spanning tree

Bellman – Ford algorithm

DFS traversal

Question 5: Consider the graph M with 3 vertices. Its adjacency matrix is shown below. Which of the following is true?

Graph M has no minimum spanning tree

Graph M has a unique minimum spanning trees of cost 2

Graph M has 3 distinct minimum spanning trees, each of cost 2

Graph M has 3 spanning trees of different costs

Question 6: Consider a undirected graph G with vertices { A, B, C, D, E}. In graph G, every edge has distinct weight. Edge CD is edge with minimum weight and edge AB is edge with maximum weight. Then, which of the following is false?

Every minimum spanning tree of G must contain CD

If AB is in a minimum spanning tree, then its removal must disconnect G

No minimum spanning tree contains AB

G has a unique minimum spanning tree

Question 7: If all the weights of the graph are positive, then the minimum spanning tree of the graph is a minimum cost subgraph.

True

False

Question 8: Consider the graph shown below. Which of the following are the edges in the MST of the given graph?

(a-c)(c-d)(d-b)(d-b)

(c-a)(a-d)(d-b)(d-e)

(a-d)(d-c)(d-b)(d-e)

(c-a)(a-d)(d-c)(d-b)(d-e)

Question 9: Which of the following is not the algorithm to find the minimum spanning tree of the given graph?

Boruvka’s algorithm

Prim’s algorithm

Kruskal’s algorithm

Bellman–Ford algorithm

Question 10: Which of the following is false?

The spanning trees do not have any cycles

MST have n – 1 edges if the graph has n edges

Edge e belonging to a cut of the graph if has the weight smaller than any other edge in the same cut, then the edge e is present in all the MSTs of the graph

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gs gs122 Minimum Spanning Tree - Minimum Spanning Tree - Quiz No.1

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