Minimum Spanning Tree


Q11.

Let G be a weighted connected undirected graph with distinct positive edge weights. If every edge weight is increasedby the same value ,then which of the following statements is/are TRUE? P: Minimum spanning tree of G does not change Q: Shortest path between any pair of vertices does not change
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Q12.

Let G be a weighted undirected graph and e be an edge with maximum weight in G. Suppose there is a minimum weight spanning tree in G containing the edge e. Which of the following statements is always TRUE?
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Q13.

Consider the following graph: Which one of the following is NOT the sequence of edges added to the minimum spanning tree using Kruskal's algorithm?
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Q14.

An undirected graph G(V, E) contains n (n>2) nodes named v1 , v2 ,...,vn. Two nodes vi , vj are connected if and only if 0\lt |i-j|\leq2. Each edge (vi,vj ) is assigned a weight i+j. A sample graph with n=4 is shown below. What will be the cost of the minimum spanning tree (MST) of such a graph with n nodes?
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Q15.

Let w be the minimum weight among all edge weights in an undirected connected graph. Let e be a specific edge of weight w . Which of the following is FALSE?
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Q16.

Consider the undirected graph below:Using Prim's algorithm to construct a minimum spanning tree starting with node A, which one of the following sequences of edges represents a possible order in which the edges would be added to construct the minimum spanning tree?
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Q17.

Let G be an undirected connected graph with distinct edge weights. Let e_{max} be the edge with maximum weight and e_{min} the edge with minimum weight. Which of the following statements is false?
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Q18.

What is the weight of a minimum spanning tree of the following graph?
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Q19.

Consider the following graph: Which one of the following cannot be the sequence of edges added, in that order, to a minimum spanning tree using Kruskal's algorithm?
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Q20.

For the undirected, weighted graph given below, which of the following sequences of edges represents a correct execution of Prim's algorithm to construct a Minimum Span?ning Tree?
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