Excursions in Modern Mathematics
9th Edition
ISBN: 9780134469096
Author: Tannenbaum
Publisher: PEARSON
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Textbook Question
Chapter 6, Problem 18E
For the weighted graph shown in
a. find the weight of edge AD.
b. find a Hamilton circuit that starts with edge AD, and give its weight.
c. find a Hamilton circuit that ends with edge DA, and give its weight.
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Students have asked these similar questions
Consider the following graph.
(b) How many trails are there from a to c?
(c) How many walks are there from a to c?
Consider the following graph, which represents the one-way airfare between five cities.
A
B
C
D
E
A
*
$220
$240
$290
$430
B
$220
*
$260
$320
$360
C
$240
$260
*
$180
$300
D
$290
$320
$180
*
$250
E
$430
$360
$300
$250
*
Graph the following to represent the information in the table. Use vertices to represent the cities and weights on appropriate edges to show the airfares.
Next, assume that you are a salesman who lives in one of the cities (pick any city except for A) and required to fly to all four of the other cities and return to your home city. Describe how you would use the Nearest Neighbor Method to determine the optimal route. What is the total cost for this Hamilton circuit?
Refer to the weighted graph attached, and answer the following:
1. The graph has an Euler path.2. What is the total weight of the path A – B – D – G – E ?
Choices: 1. True2. False3. 894. 725. 46. 907. 38. 70
Chapter 6 Solutions
Excursions in Modern Mathematics
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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- Q1- What is the minimum distance between points C and F? Q2- Which of the following is a Hamiltonian Circuit for the given graph? Q3- What is the length of the Hamiltonian Circuit described in Q2? Q4- Which vertex in the given graph has the highest degree?arrow_forwardWhen a vertex Q is connected by an edge to a vertesx K, what is the term for the relationship between Q and K A. Q and K are "isolated" B. Q and K are adjacent C. Q and K are "insecure" D. Q and K are "incident"arrow_forward45. What is the minimum distance between points C and F? A. 9 B. 10 C. 11 D. 12 46. Which of the following is a Hamiltonian Circuit for the given graph? A. AIBGCDEFHA B. DICBAIHGFED C. FIBAHGCDEF D. GFEIDCBAHG 47. What is the length of the Hamiltonian Circuit described in number 46? A. 35 B. 37 C. 39 D. 41arrow_forward
- Find the graph that matches the following hypothesis test.H0:p=17.1, Ha:p<17.1arrow_forwardFor what values of t in 10, 602 does the graph of y = c1t2 as shown have a discontinuity?arrow_forwardFor which of the two situations below is it desirable to find an Euler circuit or an efficient eulerization of a graph I. After a storm, a health department worker inspects all the houses of a small village to check for damage. II. A veteran planning a visit to all the war memorials in Washington, D.C., plots a route to follow.arrow_forward
- Consider the following graph G = (V, E) 1. List all nodes of G. 2. List all edges of G. 3. Let C be a cycle in G. C=( ? ) 4. Let T = (V, E′) be a tree such that E′⊆Earrow_forwardFind a Hamilton circuit for each graph below. Hamilton circuit for Kut Hamilton circuit for Kz Hamilton circuit for Kg:arrow_forwardanswer the following question based on given graph Q-What can one conclude from it? What is the possible result? Is it significant or not?arrow_forward
- For which values of n does the graph Cn have an Euler circuit?arrow_forwardWhich of the following is/are non-Eulerian graph? a. Graphs B C D ONLY b. Graphs B C D E c. Graph C D F ONLY d. Graphs B C D Farrow_forwardThe weight or cost of a path in a weighted graph is the sum of edge weights of a path. The shortest path from a vertex s to a vertex t is the least cost path from s to t. Given the graph below, which of the following path from s to t is the shortest path?arrow_forward
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