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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)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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**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.* - [ ] Let T be any MST of G. Then, T must contain a lightest edge in G. - [ ] Prim's algorithm can be implemented to run in time proportional to E log V in the worst case, where V and E are the number of vertices and edges in G, respectively. - [ ] Assume that two (or more) edges in G have the same weight. Then, G must have two (or more) different MSTs. - [ ] 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). - [ ] Assume that the edge weights in G are distinct. Then, the MST must contain the second lightest edge in G.
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.* - [ ] Let T be any MST of G. Then, T must contain a lightest edge in G. - [ ] Prim's algorithm can be implemented to run in time proportional to E log V in the worst case, where V and E are the number of vertices and edges in G, respectively. - [ ] Assume that two (or more) edges in G have the same weight. Then, G must have two (or more) different MSTs. - [ ] 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). - [ ] Assume that the edge weights in G are distinct. Then, the MST must contain the second lightest edge in G.
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