Question 1 : 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?
1. Every minimum spanning tree of G must contain CD
2. If AB is in a minimum spanning tree, then its removal must disconnect G
3. No minimum spanning tree contains AB
4. G has a unique minimum spanning tree
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Question 2 : If all the weights of the graph are positive, then the minimum spanning tree of the graph is a minimum cost subgraph.
1. True
2. False
3.
4.
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Question 3 : Kruskal's algorithm is used to ______
1. find minimum spanning tree
2. find single source shortest path
3. find all pair shortest path algorithm
4. traverse the graph
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Question 4 : Prim's algorithm can be efficiently implemented using _____ for graphs with greater density.
1. d-ary heap
2. linear search
3. fibonacci heap
4. binary search
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Question 5 : Consider a complete graph G with 4 vertices. The graph G has ____ spanning trees.
1. 15
2. 8
3. 16
4. 13
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Question 6 : Worst case is the worst case time complexity of Prim's algorithm if adjacency matrix is used?
1. O(log V)
2. O(V²)
3. O(E²)
4. O(V log E)
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Question 7 : Kruskal's algorithm is best suited for the sparse graphs than the prim's algorithm.
1. True
2. False
3.
4.
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Question 8 : Prim's algorithm is a ______
1. Divide and conquer algorithm
2. Greedy algorithm
3. Dynamic Programming
4. Approximation algorithm
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Question 9 : What is the time complexity of Kruskal's algorithm?
1. O(log V)
2. O(E log V)
3. O(E²)
4. O(V log E)
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Question 10 : Kruskal's algorithm is best suited for the dense graphs than the prim's algorithm.
1. True
2. False
3.
4.
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