EXCURSIONS IN MODERN MATH
EXCURSIONS IN MODERN MATH
5th Edition
ISBN: 9781323741559
Author: Tannenbaum
Publisher: PEARSON C
bartleby

Videos

Textbook Question
Book Icon
Chapter 5, 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 each vertex.

d. draw a version of the graph without crossing points.

Chapter 5, 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

Expert Solution
Check Mark
To determine

(a)

To find:

The vertex set of given graph.

Answer to Problem 1E

Solution:

The vertex set is {A,B,C,X,Y,Z}.

Explanation of Solution

In the graphical representation of routes, the location is defined as a dot in the graph. Those dots are the vertices of the graph and the collection of vertices come under the vertex set.

Given:

The given graph is,

EXCURSIONS IN MODERN MATH, Chapter 5, Problem 1E , additional homework tip  1

From the given graph, the vertices are A, B, C, X, Y and Z and the vertex set is {A,B,C,X,Y,Z}.

Expert Solution
Check Mark
To determine

(b)

To find:

The edge list of given graph.

Answer to Problem 1E

Solution:

The list of edges is AX, AY, AZ, BB, BX, BC, CX and XY.

Explanation of Solution

Given:

In the graphical representation of routes, the paths or routes are defined by the lines in the graph. Those lines are the edges of the graph.

The given graph is,

EXCURSIONS IN MODERN MATH, Chapter 5, Problem 1E , additional homework tip  2

From the given graph, the edges are AX, AY, AZ, BB, BX, BC, CX and XY.

Expert Solution
Check Mark
To determine

(c)

To find:

The degree of each vertex in given graph.

Answer to Problem 1E

Solution:

The degree on vertices are deg(A)=3, deg(B)=4, deg(C)=2, deg(X)=4, deg(Y)=2 and deg(Z)=1.

Explanation of Solution

In the graph theory, the degree of any vertex is the number of edge formed on that particular vertex.

The count for a loop on any vertex is two degree on that vertex.

Given:

The given graph is,

EXCURSIONS IN MODERN MATH, Chapter 5, Problem 1E , additional homework tip  3

From the given graph, the vertex A has 3 edges adjoined on it. The degree of vertex A is deg(A)=3.

The vertex B has 4 edges adjoined on it. The degree of vertex B is deg(B)=4.

The vertex C has 2 edges adjoined on it. The degree of vertex C is deg(C)=2.

The vertex X has 4 edges adjoined on it. The degree of vertex X is deg(X)=4.

The vertex Y has 2 edges adjoined on it. The degree of vertex Y is deg(Y)=2.

The vertex Z has 1 edge adjoined on it. The degree of vertex Z is deg(Z)=1.

Conclusion:

Thus, the degree on vertices are deg(A)=3, deg(B)=4, deg(C)=2, deg(X)=4, deg(Y)=2 and deg(Z)=1.

Expert Solution
Check Mark
To determine

(d)

To plot:

The version of the graph without crossing points

Answer to Problem 1E

Solution:

The required graph is,

EXCURSIONS IN MODERN MATH, Chapter 5, Problem 1E , additional homework tip  4

Explanation of Solution

Given:

The given graph is,

EXCURSIONS IN MODERN MATH, Chapter 5, Problem 1E , additional homework tip  5

The required graph needs to have a route in which no vertex is taken again. From the given graph, the required graph is,

EXCURSIONS IN MODERN MATH, Chapter 5, Problem 1E , additional homework tip  6

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
= 12:02 WeBWorK / 2024 Fall Rafeek MTH23 D02 / 9.2 Testing the Mean mu / 3 38 WEBWORK Previous Problem Problem List Next Problem 9.2 Testing the Mean mu: Problem 3 (1 point) Test the claim that the population of sophomore college students has a mean grade point average greater than 2.2. Sample statistics include n = 71, x = 2.44, and s = 0.9. Use a significance level of a = 0.01. The test statistic is The P-Value is between : The final conclusion is < P-value < A. There is sufficient evidence to support the claim that the mean grade point average is greater than 2.2. ○ B. There is not sufficient evidence to support the claim that the mean grade point average is greater than 2.2. Note: You can earn partial credit on this problem. Note: You are in the Reduced Scoring Period. All work counts for 50% of the original. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. . Oli wwm01.bcc.cuny.edu
>tt 1:32 > trend.1m 1m (sales > summary(trend.1m) - tt) #3###23 (i) #### Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2107.220 57.997 36.332e-16 *** tt -43.500 3.067 -14.18 7.72e-15 *** > trend = ts (fitted (trend.1m), start-start (sales), freq-frequency (sales)) sales trend ###23%23 (ii) #### as.numeric((1:32 %% 4) > X > q1 > q2 > q3 > 94 = = = = - as.numeric((1:32 %% 4) as.numeric((1:32 %% 4) as.numeric((1:32 %% 4) == 1) 2) == == 3) == 0) > season.lm = 1m (resid (trend.1m) 0+q1 + q2 + q3 + q4) #3##23%23 (iii) #### > summary(season.1m) Coefficients: Estimate Std. Error t value Pr(>|t|) q1 -38.41 43.27 -0.888 0.38232 92 18.80 43.27 0.435 0.66719 q3 -134.78 43.27 -3.115 0.00422 ** 94 154.38 43.27 3.568 0.00132 ** > season = ts (fitted (season.lm), start=start (sales), freq=frequency (sales)) > Y X season %23%23%23%23 (iv) #### >ar (Y, aic=FALSE, order.max=1) #23%23%23%23 (v) #### Coefficients: 1 0.5704 Order selected 1 sigma 2 estimated as 9431 > ar(Y, aic=FALSE,…
Please sketch questions 1, 2 and 6

Chapter 5 Solutions

EXCURSIONS IN MODERN MATH

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
Background pattern image
Math
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
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Intermediate Algebra
Algebra
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Text book image
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Text book image
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781337282291
Author:Ron Larson
Publisher:Cengage Learning
Text book image
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
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