Excursions in Modern Mathematics (8E) [Math 11008: Explorations in Modern Mathematics] (Kent State University)
10th Edition
ISBN: 9781269446716
Author: Peter Tannenbaum
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 5, Problem 55E
This exercise refers to the Fourth of July parade problem introduced in Exercise 27. Find an optimal route for the parade that starts at A and ends at B (See Fig. 5-40). Describe the route by labeling the edges 1, 2, 3, … etc. in the order they are traveled. [Hint: Start with the graph model for the parade route See Exercise 27; then find an optimal semi-eulerization of the graph that leaves A and B odd; then find an Euler path in this new graph.]
Figure 5-40
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A social worker starts from her home A, must visit clients atB, C, D, and E (in any order), and return home to A at theend of the day. The graph in Fig. 6-40 shows the distance (inmiles) between the five locations. Find an optimal tour forthis TSP, and give its cost in miles. (Hint: The edge AC ispart of an optimal tour.)
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?
Discrete Maths Oscar Levin 3rd eddition 4.1.15:
Prove that any graph with at least two vertices must have two vertices of the same degree.
ps: I'd be so glad if you include every detail of the solution.
Chapter 5 Solutions
Excursions in Modern Mathematics (8E) [Math 11008: Explorations in Modern Mathematics] (Kent State University)
Ch. 5 - For the graph shown in Fig 5-29, a.give the vertex...Ch. 5 - For the graph shown in Fig. 5-30, a.give the...Ch. 5 - For the graph shown in Fig. 5-31, 1.give the...Ch. 5 - For the graph shown in Fig. 5-32, a.give the...Ch. 5 - Consider the graph with vertex set {K,R,S,T,W} and...Ch. 5 - Consider the graph with vertex set {A,B,C,D,E} and...Ch. 5 - Consider the graph with vertex set {A,B,C,D,E} and...Ch. 5 - Consider the graph with vertex set {A,B,C,X,Y,Z}...Ch. 5 - a.Give an example of a connected graph with eight...Ch. 5 - a.Give an example of a connected graph with eight...
Ch. 5 - Consider the graph in Fig. 5-33. a. Find a path...Ch. 5 - Consider the graph in Fig. 5-33. a. Find a path...Ch. 5 - Consider the graph in Fig. 5-33. a. Find all...Ch. 5 - Consider the graph in Fig 5-34 a.Find all circuits...Ch. 5 - List all the bridges in each of the following...Ch. 5 - List all the bridges in each of the following...Ch. 5 - Consider the graph in Fig 5-35. a. List all the...Ch. 5 - Consider the graph in Fig 5-36. a. List all the...Ch. 5 - Figure 5-37 shows a map of the downtown area of...Ch. 5 - Figure 5-38 is a map of downtown Royalton, showing...Ch. 5 - A night watchman must walk the streets of the...Ch. 5 - A mail carrier must deliver mail on foot along the...Ch. 5 - Six teams (A,B,C,D,E,andF) are entered in a...Ch. 5 - The Kangaroo Lodge of Madison Country has 10...Ch. 5 - Table 5-3 summarizes the Facebook friendships...Ch. 5 - The Dean of students office wants to know how the...Ch. 5 - Figure 5-40 shows the downtown area of the small...Ch. 5 - Prob. 28ECh. 5 - In Exercise 29 through 34 choose from the...Ch. 5 - In Exercise 29 through 34 choose from the...Ch. 5 - In Exercise 29 through 34 choose from the...Ch. 5 - In Exercises 29 through 34 choose from the...Ch. 5 - In Exercise 29 through 34 choose from the...Ch. 5 - In Exercise 29 through 34 choose from the...Ch. 5 - Find the Euler circuit for the graph in Fig.5-47....Ch. 5 - Find the Euler circuit for the graph in Fig.5.48_....Ch. 5 - Find the Euler path for the graph in Fig.5-49_....Ch. 5 - Find the Euler path for the graph in Fig.5-50....Ch. 5 - Find an Euler circuit for the graph in Fig 5-51....Ch. 5 - Find the Euler circuit for the graph in Fig 5-52....Ch. 5 - Suppose you are using Fleurys algorithm to find an...Ch. 5 - Suppose you are using Fleurys algorithm to find an...Ch. 5 - Find an optimal eulerization for the graph in Fig...Ch. 5 - Find an optimal eulerization for the graph in Fig....Ch. 5 - Find an optimal eulerization for the graph in Fig....Ch. 5 - Find an optimal eulerization for the graph in Fig...Ch. 5 - Find an optimal semi-eulerization for the graph in...Ch. 5 - Find an optimal semi-eulerization for the graph in...Ch. 5 - Prob. 49ECh. 5 - Prob. 50ECh. 5 - Prob. 51ECh. 5 - Prob. 52ECh. 5 - A security guard must patrol on foot the streets...Ch. 5 - A mail carrier must deliver mail on foot along the...Ch. 5 - This exercise refers to the Fourth of July parade...Ch. 5 - This exercise refers to the Fourth of July parade...Ch. 5 - Consider the following puzzle: You must trace Fig...Ch. 5 - a.Explain why in every graph the sum of the...Ch. 5 - Prob. 59ECh. 5 - Regular graphs. A graph is called regular if every...Ch. 5 - Suppose G is a disconnected graph with exactly two...Ch. 5 - Consider the following game. You are given N...Ch. 5 - Figure 5-59 shows a map of the downtown area of...Ch. 5 - Kissing circuits. When two circuits in a graph...Ch. 5 - Prob. 65ECh. 5 - Exercises 66 through 68 refer to Example 5.23 . In...Ch. 5 - Exercises 66 through 68 refer to Example 5.23 . In...Ch. 5 - Exercises 66 through 68 refer to Example 5.23 . In...Ch. 5 - This exercise comes to you courtesy of Euler...Ch. 5 - Running Suppose G is a connected graph with N...Ch. 5 - Running Suppose G is a connected graph with N2...Ch. 5 - Running Complete bipartite graphs. A complete...Ch. 5 - Running Suppose G is a simple graph with N...
Knowledge Booster
Learn more about
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
- Recall that the distance between two vertices, u and v, is the length of a shortest path between u and v. What is the maximum possible distance between two vertices in G? Provide an example of two vertices that are this distance apart, but not need to justify that this is the maximum possible.arrow_forwardCan someone help me find the questions listed in the screenshot. By using the NorthWest Method and using loop to get to the optimal w.arrow_forwardScott and Associates, Inc., is an accounting firm that has three new clients. Project leaders will be assigned to the three clients. Based on the different backgrounds and experiences of the leaders, the various leader–client assignments differ in terms of projected completion times. The possible assignments and the estimated completion times in days are as follows: Requireda. Develop a network representation of this problem.b. Find the optimal solution using the Hungarian method. What is the total time required?arrow_forward
- Consider the complete bipartite graph K4,3. a) Does it have a Hamiltonian path? b) Does it have a Hamiltonian cycle? c) What is maximum size of a matching in this graph? d) What is minimum size of a vertex cover in this graph?arrow_forwardConsider the following shortest path problem. Find the total distance of the shortest route from Node 1 to Node 6. a.600 b.450 c.750 d.550 e.500arrow_forwardfind the length of a shortest path and a shortestpath between each pair of vertices in the weighted graph. question 3 and 5arrow_forward
- Solve the shortest path problems shown in the attached picture by hand using the original implementation of Dijkstra's algorithm. Count the number of distance updates, provide the shortest path solution and the hand-drawn trees of shortest paths for (a) and (b).arrow_forwardDiscrete Maths Oscar Levin 3rd eddition 4.1.16: Suppose G is a connected graph with n > 1 vertices and n − 1 edges. Prove that G has a vertex of degree 1. ps: I'd be so glad if you include every detail of the solutionarrow_forwardIt is obvious that for a bipartite graph to contain a perfect matching, it is necessary that |A| = |B|. Show that if every node has the same degree, then this is indeed so.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
Graph Theory: Euler Paths and Euler Circuits; Author: Mathispower4u;https://www.youtube.com/watch?v=5M-m62qTR-s;License: Standard YouTube License, CC-BY
WALK,TRIAL,CIRCUIT,PATH,CYCLE IN GRAPH THEORY; Author: DIVVELA SRINIVASA RAO;https://www.youtube.com/watch?v=iYVltZtnAik;License: Standard YouTube License, CC-BY