Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
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Textbook Question
Chapter 6, Problem 2E
For the graph shown in Fig. 6-20,
a. find three different Hamilton circuits.
b. find a Hamilton path that starts at A and ends at B.
c. find a Hamilton path that starts at F and ends at I.
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Students have asked these similar questions
Which of the following is NOT a circuit in the graph?
A
B
F
E
О сс
O ABFEA
O BFDCB
O None of the Above
Consider the following rooms from a hotel:
D2
Room 217
Room 218
D1
D3
Hallway
D6
D4
Room 318
Room 317
D5
A. Please draw a graph that shows how the various rooms are connected to each-other by
doorways (count the Hallway as a normal room)
B. Please give a walk from room 217 to room 318 that is not a trail.
c. Is there an Euler circuit through these rooms? 1.e., is it possible to walk around the rooms,
starting and ending in the same room, and visiting every room while passing through each
door exactly once? Please give such a circuit, if one exists, or say how you know that no
such circuit exists.
Which are circuits in the graph? If not, why not?
(a) E→ F→ A B C D
(b) B→CD
F→A → B
(c) A D E F→A
(d) CD
F→B →D
(e) F→E
F→D→E→F
—
B
D
OA. Yes, it is a circuit.
OB. No, it is not a circuit. It does not begin and end at the same vertex.
OC. No, it is not a circuit. The edge joining vertices is used more than once.
(Use a comma to separate answers as needed.)
F
(Use a comma to separate answers as needed.)
(d) Is CD → F→B→ Da circuit? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. Yes, it is a circuit.
OB. No, it is not a circuit. The edge joining vertices is used more than once.
(Use a comma to separate answers as needed.)
OC. No, it is not a circuit. There is no edge joining vertices
(Use a comma to separate answers as needed.)
OD. No, it is not a circuit. It does not begin and end at the same vertex.
E
G
OD. No, it is not a circuit. There is no edge joining vertices
(Use a comma to separate answers as needed.)
(e) Is F→ E→F→D E F…
Chapter 6 Solutions
Excursions in Modern Mathematics (9th Edition)
Ch. 6 - For the graph shown in Fig. 6-19, a.find three...Ch. 6 - For the graph shown in Fig. 6-20, a.find three...Ch. 6 - Find all possible Hamilton circuits in the graph...Ch. 6 - Find all possible Hamilton circuits in the graph...Ch. 6 - For the graph shown in Fig.6-23, a. find a...Ch. 6 - For the graph shown in Fig.6-24, a. find a...Ch. 6 - Suppose D,G,E,A,H,C,B,F,D is a Hamilton circuit in...Ch. 6 - Suppose G,B,D,C,A,F,E,G is a Hamilton circuit in a...Ch. 6 - Consider the graph in Fig. 6-25. a. Find the five...Ch. 6 - Consider the graph in Fig.6-26. a. Find all the...
Ch. 6 - Consider the graph in Fig.6-27. a. Find all the...Ch. 6 - Prob. 12ECh. 6 - For the graph in Fig.6-29 a. find a Hamilton path...Ch. 6 - For the graph in Fig.6-30 a. find a Hamilton path...Ch. 6 - Explain why the graph shown in Fig.6-31 has...Ch. 6 - Explain why the graph shown in Fig.6-32 has...Ch. 6 - For the weighted shown in Fig 6-33, a.find the...Ch. 6 - For the weighted graph shown in Fig6-34, a.find...Ch. 6 - For the weighted graph shown in Fig6-35, a.find a...Ch. 6 - For the weighted graph shown in Fig6-36, a.find a...Ch. 6 - Suppose you have a supercomputer that can generate...Ch. 6 - Suppose you have a supercomputer that can generate...Ch. 6 - Prob. 23ECh. 6 - a. How many edges are there in K200? b. How many...Ch. 6 - In each case, find the value of N. a. KN has 120...Ch. 6 - In each case, find the value of N. a. KN has 720...Ch. 6 - Find an optimal tour for the TSP given in...Ch. 6 - Find an optimal tour for the TSP given in...Ch. 6 - A truck must deliver furniture to stores located...Ch. 6 - A social worker starts from her home A, must visit...Ch. 6 - You are planning to visit four cities A, B, C, and...Ch. 6 - An unmanned rover must be routed to visit four...Ch. 6 - For the weighted graph shown in Fig.6-41, i find...Ch. 6 - A delivery service must deliver packages at...Ch. 6 - Prob. 35ECh. 6 - A space mission is scheduled to visit the moons...Ch. 6 - This exercise refers to the furniture truck TSP...Ch. 6 - This exercise refers to the social worker TSP...Ch. 6 - Darren is a sales rep whose territory consists of...Ch. 6 - The Platonic Cowboys are a country and western...Ch. 6 - Find the repetitive nearest-neighbor tour and give...Ch. 6 - Prob. 42ECh. 6 - This exercise is a continuation of Darrens sales...Ch. 6 - This exercise is a continuation of the Platonic...Ch. 6 - Prob. 45ECh. 6 - Prob. 46ECh. 6 - Find the cheapest-link tour and give its cost for...Ch. 6 - Find the cheapest-link tour for the social worker...Ch. 6 - For the Brute-Force Bandits concert tour discussed...Ch. 6 - For the weighted graph shown in Fig.6-47, find the...Ch. 6 - For Darrens sales trip problem discussed in...Ch. 6 - For the Platonic Cowboys concert tour discussed in...Ch. 6 - A rover on the planet Mercuria has to visit six...Ch. 6 - A robotic laser must drill holes on five sites A,...Ch. 6 - Prob. 55ECh. 6 - Prob. 56ECh. 6 - Suppose that in solving a TSP you find an...Ch. 6 - Prob. 58ECh. 6 - Prob. 59ECh. 6 - Prob. 60ECh. 6 - Prob. 61ECh. 6 - If the number of edges in K500 is x and the number...Ch. 6 - Explain why the cheapest edge in any graph is...Ch. 6 - a. Explain why the graph that has a bridge cannot...Ch. 6 - Julie is the marketing manager for a small...Ch. 6 - 66. m by n grid graphs. An m by n grid graph...Ch. 6 - Complete bipartite graphs. A complete bipartite...Ch. 6 - Prob. 68ECh. 6 - Diracs theorem. If G is a connected graph with N...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Which of the following graphs have Euler circuits? U I H J G Y K A: Has Euler circuit. B: Has Euler circuit. N R N L S U R C: Has Euler circuit. D: Has Euler circuit.arrow_forwardWhich of the following graphs DOES NOT have a Hamilton circuit? Select one: a. b. w C. D G F B E A Garrow_forwardUse the figure below to answer the following question(s). E B B B #4 D G OE OE F F Graph 1 Graph 2 Graph 3 Which of the graphs has an Euler path but no Euler circuit? Select one: a. Graph 2 only b. Graph 3 only C. none of these d. Graphs 1 and 2 e. Graph 1 onlyarrow_forward
- Consider the following graph: Vz V, e, Vz es es Vs eu 1. Please give a walk from v, to v4 that is not a trail. 2. Please give a path from vị to V4. 3. Please give a closed walk from v4 to v4 that is not a circuit. 4. Please give a simple circuit from vi to v1.arrow_forwardWhich of the following graphs have Euler circuits or Euler trails? K M L N I L H G N M A: Has Euler trail. A: Has Euler circuit. I Q 0 P OC: Has Euler trail. OC: Has Euler circuit. F H R S R S T V U B: Has Euler trail. B: Has Euler circuit. 0 U T D: Has Euler trail. D: Has Euler circuit. Narrow_forwardWhich of the following graphs have hamiltonian circuits? F S E G T DA C 0 U D H V M C G P 0 E H R I B D S C T B Karrow_forward
- Laarni is planning a trip. She wants to fly outof Charlotte, visit New York, visit Hollywood,and end up at her parent's home in Dallas.Which graph would be best for this scenario?A.Euler tourB. Hamiltonian cycleC. Hamiltonian pathD. Euler patharrow_forwardRefer to the figure below. a. Find a closed path of length 4 starting at vertex v2. b. Find a cycle of length 5 starting at vertex V1. c. Find a circuit that is not a cycle at vertex V4. VI V6 V5 V2 VA V 3arrow_forwardWhich of the following graphs have Euler circuits or Euler trails? K K I I P OA: Has Euler trail. O A: Has Euler circuit. B: Has Euler trail. O B: Has Euler circuit. P R N U R ) C: Has Euler trail. C: Has Euler circuit. D: Has Euler trail. OD: Has Euler circuit.arrow_forward
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