Problem 1E: For the graph shown in Fig 5-29, a.give the vertex set. b.give the edge list. c.give the degree of... Problem 2E: For the graph shown in Fig. 5-30, a.give the vertex set. b.give the edge list. c.give the degree of... Problem 3E: For the graph shown in Fig. 5-31, 1.give the vertex set. 2.give the edge list. 3.give the degree of... Problem 4E: For the graph shown in Fig. 5-32, a.give the vertex set. b.give the edge list. c.give the degree of... Problem 5E: Consider the graph with vertex set {K,R,S,T,W} and edge list RS, RT, TT, TS, SW, WW, WS. Draw two... Problem 6E: Consider the graph with vertex set {A,B,C,D,E} and edge list AC, AE, BD, BE, CA, CD, CE, DE. Draw... Problem 7E: Consider the graph with vertex set {A,B,C,D,E} and edge list AD, AE, BC, BD, DD, DE. Without drawing... Problem 8E: Consider the graph with vertex set {A,B,C,X,Y,Z} and edge list AX, AY, AZ, BB, CX, CY, CZ, YY.... Problem 9E: a.Give an example of a connected graph with eight vertices such that each vertex has degree 2.... Problem 10E: a.Give an example of a connected graph with eight vertices: six of degree 2 and two of degree 3.... Problem 11E: Consider the graph in Fig. 5-33. a. Find a path from C to F passing through vertex B but not through... Problem 12E: Consider the graph in Fig. 5-33. a. Find a path from D to E passing through vertex G only once. b.... Problem 13E: Consider the graph in Fig. 5-33. a. Find all circuits of length 1. Hint: Loops are circuits of... Problem 14E: Consider the graph in Fig 5-34 a.Find all circuits of length 1. Hint: Loops are circuits of length... Problem 15E: List all the bridges in each of the following graphs: a. the graph in Fig. 5-33. b. the graph with... Problem 16E: List all the bridges in each of the following graphs: a. the graph in Fig. 5-34 b. the graph with... Problem 17E: Consider the graph in Fig 5-35. a. List all the bridges in this graph. b. If you remove all the... Problem 18E: Consider the graph in Fig 5-36. a. List all the bridges in this graph. b. If you remove all the... Problem 19E: Figure 5-37 shows a map of the downtown area of the picturesque hamlet of Kingsburg, with the Kings... Problem 20E: Figure 5-38 is a map of downtown Royalton, showing the Royalton River running through the downtown... Problem 21E: A night watchman must walk the streets of the Green Hills subdivision shown in Fig. 5-39. The night... Problem 22E: A mail carrier must deliver mail on foot along the streets of the Green Hills subdivision shown in... Problem 23E: Six teams (A,B,C,D,E,andF) are entered in a softball tournament. The top two seeded teams (AandB)... Problem 24E: The Kangaroo Lodge of Madison Country has 10 members A,B,C,D,E,F,G,H,I and J. The club has five... Problem 25E: Table 5-3 summarizes the Facebook friendships between a group of eight individuals an F indicates... Problem 26E: The Dean of students office wants to know how the seven general education courses selected by... Problem 27E: Figure 5-40 shows the downtown area of the small village of Kenton. The village wants to have a... Problem 28E Problem 29E: In Exercise 29 through 34 choose from the following answers and provide a short explanation for your... Problem 30E: In Exercise 29 through 34 choose from the following answers and provide a short explanation for your... Problem 31E: In Exercise 29 through 34 choose from the following answers and provide a short explanation for your... Problem 32E: In Exercises 29 through 34 choose from the following answers and provide a short explanation for... Problem 33E: In Exercise 29 through 34 choose from the following answers and provide a short explanation for your... Problem 34E: In Exercise 29 through 34 choose from the following answers and provide a short explanation for your... Problem 35E: Find the Euler circuit for the graph in Fig.5-47. Show the answer by labeling the edges 1, 2, 3, and... Problem 36E: Find the Euler circuit for the graph in Fig.5.48_. Show your answer by labeling the edges 1, 2, 3,... Problem 37E: Find the Euler path for the graph in Fig.5-49_. Show your answer by labeling the edges 1, 2, 3, and... Problem 38E: Find the Euler path for the graph in Fig.5-50. Show your answer by labeling the edges 1, 2, 3, and... Problem 39E: Find an Euler circuit for the graph in Fig 5-51. Use B as the starting and ending point of the... Problem 40E: Find the Euler circuit for the graph in Fig 5-52. Use P as the starting and ending vertex of the... Problem 41E: Suppose you are using Fleurys algorithm to find an Euler circuit for a graph and you are in middle... Problem 42E: Suppose you are using Fleurys algorithm to find an Euler circuit for a graph and you are in middle... Problem 43E: Find an optimal eulerization for the graph in Fig 5-54. Figure 5-54 Problem 44E: Find an optimal eulerization for the graph in Fig. 5-55. Figure 5-55 Problem 45E: Find an optimal eulerization for the graph in Fig. 5-56. Figure 5-56 Problem 46E: Find an optimal eulerization for the graph in Fig 5-57 Figure 5-57 Problem 47E: Find an optimal semi-eulerization for the graph in Fig. 5-56. You are free to choose the starting... Problem 48E: Find an optimal semi-eulerization for the graph in Fig. 5-57. You are free to choose the starting... Problem 49E Problem 50E Problem 51E Problem 52E Problem 53E: A security guard must patrol on foot the streets of the Green Hills subdivision shown in Fig. 5-39.... Problem 54E: A mail carrier must deliver mail on foot along the streets of the Green Hills subdivision shown in... Problem 55E: This exercise refers to the Fourth of July parade problem introduced in Exercise 27. Find an optimal... Problem 56E: This exercise refers to the Fourth of July parade problem introduced in Exercise 27. Find an optimal... Problem 57E: Consider the following puzzle: You must trace Fig 5-58 without retracing any lines. We know this is... Problem 58E: a.Explain why in every graph the sum of the degrees of all vertices equals twice the number of... Problem 59E Problem 60E: Regular graphs. A graph is called regular if every vertex has the same degree. Let G be a connected... Problem 61E: Suppose G is a disconnected graph with exactly two odd vertices. Explain why the two odd vertices... Problem 62E: Consider the following game. You are given N vertices and are required to build a graph by adding... Problem 63E: Figure 5-59 shows a map of the downtown area of the picturesque hamlet of Kingsburg. You have been... Problem 64E: Kissing circuits. When two circuits in a graph have no edges in common but share a common vertex v,... Problem 65E Problem 66E: Exercises 66 through 68 refer to Example 5.23 . In this example, the problem is to find an optimal... Problem 67E: Exercises 66 through 68 refer to Example 5.23 . In this example, the problem is to find an optimal... Problem 68E: Exercises 66 through 68 refer to Example 5.23 . In this example, the problem is to find an optimal... Problem 69E: This exercise comes to you courtesy of Euler himself. Here is the question in Eulers own words,... Problem 70E: Running Suppose G is a connected graph with N vertices, all of even degree. Let k denote the number... Problem 71E: Running Suppose G is a connected graph with N2 even vertices and two odd vertices. Let k denote the... Problem 72E: Running Complete bipartite graphs. A complete bipartite graph is a graph having the property that... Problem 73E: Running Suppose G is a simple graph with N vertices (N2). Explain why G must have at least two... format_list_bulleted
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning