The graph below is used for problems 7, 8 and 9. A 3 B 20 C 7 G 12 `17 26 D 29 E 8 F 7. A mathematician applies Prim's Algorithm to find a minimum spanning tree for the weighted graph starting at vertex D. The order of the edges picked so far is AD, AB, BE, and EF. The next edge selected when applying Prim's Algorithm should be а) BF b) FG c) CG d) CE 8. What is the total weight of the tree that uses the edges DE, CE, CG, FG and BF? a) 93 b) 92 c) 91 d) 90 9. The tree described in problem #8 is a spanning tree. a) True b) False 2.

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.3: Rules For Addition
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The graph below is used for problems 7, 8 and 9.
A
3
B
20
C
7
G
12
`17
26
D
29
E
8
F
7. A mathematician applies Prim's Algorithm to find a minimum spanning tree for
the weighted graph starting at vertex D. The order of the edges picked so far is
AD, AB, BE, and EF. The next edge selected when applying Prim's Algorithm
should be
а) BF
b) FG
с) CG
d) CE
8. What is the total weight of the tree that uses the edges DE, CE, CG, FG and BF?
а) 93
b) 92
c) 91
d) 90
9. The tree described in problem #8 is a spanning tree.
a) True
b) False
2.
Transcribed Image Text:The graph below is used for problems 7, 8 and 9. A 3 B 20 C 7 G 12 `17 26 D 29 E 8 F 7. A mathematician applies Prim's Algorithm to find a minimum spanning tree for the weighted graph starting at vertex D. The order of the edges picked so far is AD, AB, BE, and EF. The next edge selected when applying Prim's Algorithm should be а) BF b) FG с) CG d) CE 8. What is the total weight of the tree that uses the edges DE, CE, CG, FG and BF? а) 93 b) 92 c) 91 d) 90 9. The tree described in problem #8 is a spanning tree. a) True b) False 2.
A person starting in Columbus must visit Great Falls, Odessa, and
Brownsville (although not necessarily in that order), and then return home to
Columbus in one car trip. The road mileage between the cities is shown.
Great Falls
Columbus
Odessa
Brownsville
Columbus
102
79
56
---
Great Falls
102
47
69
---
Odessa
79
47
72
---
Brownsville
56
69
72
a) Draw a weighted graph that represents this problem in the space below. Use
the first letter of the city when labeling each vertex.
b) Find the weight (distance) of the Hamiltonian circuit formed using the nearest
neighbor algorithm. Give the vertices in the circuit in the order they are
visited in the circuit as well as the total weight (distance) of the circuit.
Remember to include the unit of measure in your final answer.
4.
Find a Hamiltonian circuit in the following graph. (There is more than
one possible answer.) Either clearly mark the path you take with directional
arrows and numbers or list the vertices in the order that you visit them.
A
в
D
E
Transcribed Image Text:A person starting in Columbus must visit Great Falls, Odessa, and Brownsville (although not necessarily in that order), and then return home to Columbus in one car trip. The road mileage between the cities is shown. Great Falls Columbus Odessa Brownsville Columbus 102 79 56 --- Great Falls 102 47 69 --- Odessa 79 47 72 --- Brownsville 56 69 72 a) Draw a weighted graph that represents this problem in the space below. Use the first letter of the city when labeling each vertex. b) Find the weight (distance) of the Hamiltonian circuit formed using the nearest neighbor algorithm. Give the vertices in the circuit in the order they are visited in the circuit as well as the total weight (distance) of the circuit. Remember to include the unit of measure in your final answer. 4. Find a Hamiltonian circuit in the following graph. (There is more than one possible answer.) Either clearly mark the path you take with directional arrows and numbers or list the vertices in the order that you visit them. A в D E
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