Question Which of the following statements about minimum spanning trees (MSTS) are true for every edge-weighted graph G? Assume that G contains at least 3 vertices, is connected, and has no parallel edges or self-loops Do not assume the edge weights are distinct unless this is specifically stated. Answer Mark all that apply. O Let T be any MST of G. Then, T must contain a lightest edge in G. O Prim's algorithm can be implemented to run in time proportional to E log V in the worst case, where V and E and the number of vertices and edges in G, respectively. U Assume that two (or more) edges in G have the same weight. Then, G must have two (or more) different MSTS. O Assume that the edge weights in G are distinct. Let w(e) > 0 denote the weight of edge e in G. Then, T is a maximum spanning tree of G if and only if T is a minimum spanning tree in the edge-weighted graph G' with weights w'(e) = -w(e). U Assume that the edge weights in G are distinct. Then, the MST must contain the second lightest edge in G.
Question Which of the following statements about minimum spanning trees (MSTS) are true for every edge-weighted graph G? Assume that G contains at least 3 vertices, is connected, and has no parallel edges or self-loops Do not assume the edge weights are distinct unless this is specifically stated. Answer Mark all that apply. O Let T be any MST of G. Then, T must contain a lightest edge in G. O Prim's algorithm can be implemented to run in time proportional to E log V in the worst case, where V and E and the number of vertices and edges in G, respectively. U Assume that two (or more) edges in G have the same weight. Then, G must have two (or more) different MSTS. O Assume that the edge weights in G are distinct. Let w(e) > 0 denote the weight of edge e in G. Then, T is a maximum spanning tree of G if and only if T is a minimum spanning tree in the edge-weighted graph G' with weights w'(e) = -w(e). U Assume that the edge weights in G are distinct. Then, the MST must contain the second lightest edge in G.
Computer Networking: A Top-Down Approach (7th Edition)
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Which of the following statements about minimum spanning trees (MSTS) are true for every edge-weighted graph G? Assume that G contains at least 3 vertices, is connected, and has no parallel edges or self-loops.
Do not assume the edge weights are distinct unless this is specifically stated.
Answer
Mark all that apply.
O Let T be any MST of G. Then, T must contain a lightest edge in G.
O Prim's algorithm can be implemented to run in time proportional to E log V in the worst case, where V and E and the number of vertices and edges in G, respectively.
O Assume that two (or more) edges in G have the same weight. Then, G must have two (or more) different MSTS.
O Assume that the edge weights in G are distinct. Let w(e) > 0 denote the weight of edge e in G. Then, Tis a maximum spanning tree of G if and only if T is a minimum spanning tree in the edge-weighted graph G' with weights w'(e) = -w(e).
D Assume that the edge weights in G are distinct. Then, the MST must contain the second lightest edge in G.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88167701-6d3f-46b8-9f75-5ab21a2347bf%2Facd906e1-b660-441a-9e9d-eb0f380e3b73%2Fbvt9o5k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question
Which of the following statements about minimum spanning trees (MSTS) are true for every edge-weighted graph G? Assume that G contains at least 3 vertices, is connected, and has no parallel edges or self-loops.
Do not assume the edge weights are distinct unless this is specifically stated.
Answer
Mark all that apply.
O Let T be any MST of G. Then, T must contain a lightest edge in G.
O Prim's algorithm can be implemented to run in time proportional to E log V in the worst case, where V and E and the number of vertices and edges in G, respectively.
O Assume that two (or more) edges in G have the same weight. Then, G must have two (or more) different MSTS.
O Assume that the edge weights in G are distinct. Let w(e) > 0 denote the weight of edge e in G. Then, Tis a maximum spanning tree of G if and only if T is a minimum spanning tree in the edge-weighted graph G' with weights w'(e) = -w(e).
D Assume that the edge weights in G are distinct. Then, the MST must contain the second lightest edge in G.
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