BuyFind*arrow_forward*

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.1, Problem 25ES

Textbook Problem

2 views

Transportation For the train routes given in Exercise 1, is it possible to travel along all of the train routes without traveling along any route twice? Explain how you reached your conclusion.

To determine

To determine if it is possible to travel along all of the train routes without traveling along any route twice.

**Given information:**

Given, an "X" in the given table indicates a direct train route between the corresponding cities.

A graph is to be made where each vertex represents a city and an edge connects two vertices if there is a train route between the corresponding cities.

â€ƒâ€ƒ

And the graph is,

â€ƒâ€ƒ

**Calculation:**

It is possible to travel along all of the train routes without traveling along any route twice if the graph satisfies the condition of either Euler circuit or Euler path.

An Eulerian graph (that starts and ends at the same vertex) is said to be Euler circuit if it uses every edge, but only once. (i.e. no edge is used more than once).

Euler path is defined as the path in a connected graph that has exactly two vertices of odd degree with all the remaining vertices of even degree and the path starts at one of the vertices with odd degree and ends at the other vertex with odd degree.

Firstly, the graph is checked to know whether it satisfies to be an Eulerian graph.

A graph is said to be Eulerian graph if it is a connected graph and every vertex of the graph has even degree...

Mathematical Excursions (MindTap Course List)

Show all chapter solutions

Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - Explain why the following pen-tracing puzzle is...Ch. 5.1 - Transportation An X in the table below indicates a...Ch. 5.1 - Transportation The table below shows the nonstop...Ch. 5.1 - Social Network A group of friends is represented...Ch. 5.1 - Baseball The local Little League baseball teams...Ch. 5.1 - Determine (a) the number of edges in the graph,...

Ch. 5.1 - Determine (a) the number of edges in the graph,...Ch. 5.1 - Determine (a) the number of edges in the graph,...Ch. 5.1 - Determine (a) the number of edges in the graph,...Ch. 5.1 - Determine whether the two graphs are equivalent.Ch. 5.1 - Determine whether the two graphs are equivalent.Ch. 5.1 - Determine whether the two graphs are equivalent.Ch. 5.1 - Determine whether the two graphs are equivalent.Ch. 5.1 - Explain why the following two graphs cannot be...Ch. 5.1 - Label the vertices of the second graph so that it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - (a) determine whether the graph is Eulerian. If it...Ch. 5.1 - Parks in Exercises 23 and 24, a map of a park is...Ch. 5.1 - Parks in Exercises 23 and 24, a map of a park is...Ch. 5.1 - Transportation For the train routes given in...Ch. 5.1 - Transportation For the direct air flights given in...Ch. 5.1 - Pets The diagram below shows the arrangement of a...Ch. 5.1 - Transportation A subway map is shown below. Is it...Ch. 5.1 - Architecture, a floor plan of a museum is shown....Ch. 5.1 - Architecture, a floor plan of a museum is shown....Ch. 5.1 - Degrees of Separation In the graph below, an edge...Ch. 5.1 - Social Network In the graph below, an edge...Ch. 5.1 - Bridges of a Graph An edge of a connected graph is...Ch. 5.1 - Travel A map of South America is shown at the...Ch. 5.2 - Continue investigating Hamiltonian circuits in...Ch. 5.2 - Use the greedy algorithm and the weighted graph...Ch. 5.2 - Use the edge-picking algorithm to find a...Ch. 5.2 - Use Dirac's theorem to verify that the graph is...Ch. 5.2 - Use Dirac's theorem to verify that the graph is...Ch. 5.2 - Use Dirac's theorem to verify that the graph is...Ch. 5.2 - Use Dirac's theorem to verify that the graph is...Ch. 5.2 - Transportation For the train routes given in...Ch. 5.2 - Transportation For the direct air flights given in...Ch. 5.2 - Use trial and error to find two Hamiltonian...Ch. 5.2 - Use trial and error to find two Hamiltonian...Ch. 5.2 - Use trial and error to find two Hamiltonian...Ch. 5.2 - Use trial and error to find two Hamiltonian...Ch. 5.2 - Use the greedy algorithm to find a Hamiltonian...Ch. 5.2 - Use the greedy algorithm to find a Hamiltonian...Ch. 5.2 - Use the greedy algorithm to find a Hamiltonian...Ch. 5.2 - Use the greedy algorithm to find a Hamiltonian...Ch. 5.2 - Use the edge-picking algorithm to find a...Ch. 5.2 - Use the edge-picking algorithm to find a...Ch. 5.2 - Use the edge-picking algorithm to find a...Ch. 5.2 - Use the edge-picking algorithm to find a...Ch. 5.2 - Travel A company representative lives in...Ch. 5.2 - Travel A tourist is staying in Toronto, Canada,...Ch. 5.2 - Travel Use the edge-picking algorithm to design a...Ch. 5.2 - Travel Use the edge-picking algorithm to design a...Ch. 5.2 - Travel Nicole wants to tour Asia. She will start...Ch. 5.2 - Travel The prices for traveling between five...Ch. 5.2 - Travel Use the edge-picking algorithm to find a...Ch. 5.2 - Travel Use the edge-picking algorithm to find a...Ch. 5.2 - Route Planning Brian needs to visit the pet store,...Ch. 5.2 - Route Planning A bike messenger needs to deliver...Ch. 5.2 - Scheduling A research company has a large...Ch. 5.2 - Computer Networks A small office wishes to network...Ch. 5.2 - Route Planning A security officer patrolling a...Ch. 5.2 - Route Planning A city engineer needs to inspect...Ch. 5.2 - Draw a connected graph with six vertices that has...Ch. 5.2 - Assign weights to the edges of the following...Ch. 5.3 - The tetrahedron in figure 5.20 consists of four...Ch. 5.3 - The following graph is the projection of one ofthe...Ch. 5.3 - If we form a graph by a projection of the...Ch. 5.3 - Give a reason why the graph below Cannot be the...Ch. 5.3 - Show that the graph is planar by finding a planar...Ch. 5.3 - Show that the graph is planar by finding a planar...Ch. 5.3 - Show that the graph is planar by finding a planar...Ch. 5.3 - Show that the graph is planar by finding a planar...Ch. 5.3 - Show that the graph is planar by finding a planar...Ch. 5.3 - Show that the graph is planar by finding a planar...Ch. 5.3 - Show that the graph is planar by finding a planar...Ch. 5.3 - Show that the graph is planar by finding a planar...Ch. 5.3 - Show that the graph is not planar.Ch. 5.3 - Show that the graph is not planar.Ch. 5.3 - Show that the graph is not planar.Ch. 5.3 - Show that the graph is not planar.Ch. 5.3 - Show that the following graph contracts to K5.Ch. 5.3 - Show that the following graph contracts to the...Ch. 5.3 - Show that the graph is not planar by finding a...Ch. 5.3 - Show that the graph is not planar by finding a...Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - Count the number of vertices, edges, and faces,...Ch. 5.3 - If a planar drawing of a graph has 15 edges and 8...Ch. 5.3 - If a planar drawing of a graph has 100 vertices...Ch. 5.3 - Sketch a planar graph (without multiple edges or...Ch. 5.3 - Sketch a planar graph (without multiple edges or...Ch. 5.3 - Explain why it is not possible to draw a planar...Ch. 5.3 - If a planar drawing of a graph has twice as many...Ch. 5.3 - Show that the complete graph with five vertices,...Ch. 5.3 - Dual Graph Every planar graph has what is called a...Ch. 5.4 - A one-way road ends at a two-way street. The...Ch. 5.4 - A one-way road intersects a two-way road in a...Ch. 5.4 - A two-way road intersects another two-way road in...Ch. 5.4 - Map Coloring A fictional map of the countries of a...Ch. 5.4 - Map Coloring A fictional map of the countries of a...Ch. 5.4 - Map Coloring A fictional map of the countries of a...Ch. 5.4 - Map Coloring A fictional map of the countries of a...Ch. 5.4 - Map Coloring Represent the map by a graph and find...Ch. 5.4 - Map Coloring Represent the map by a graph and find...Ch. 5.4 - Map Coloring Represent the map by a graph and find...Ch. 5.4 - Map Coloring Represent the map by a graph and find...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Show that the graph is 2-colorable by finding a...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Determine (by trial and error) the chromatic...Ch. 5.4 - Scheduling Six student clubs need to hold meetings...Ch. 5.4 - Scheduling Eight political committees must meet on...Ch. 5.4 - Scheduling Six different groups of children would...Ch. 5.4 - Scheduling Five different charity organizations...Ch. 5.4 - Scheduling Students in a film class have...Ch. 5.4 - Animal Housing A researcher has discovered six new...Ch. 5.4 - Wi-Fi Stations An office building is installing...Ch. 5.4 - Map Coloring Draw a map of a fictional continent...Ch. 5.4 - If the chromatic number of a graph with five...Ch. 5.4 - Edge Coloring In this section, we colored vertices...Ch. 5.4 - Scheduling Edge colorings, as explained in...Ch. 5 - (a) determine the number of edges in the graph,...Ch. 5 - (a) determine the number of edges in the graph,...Ch. 5 - Soccer In the table below, an X indicates teams...Ch. 5 - Each vertex in the graph at the left represents a...Ch. 5 - Determine whether the two graphs are equivalent.Ch. 5 - Determine whether the two graphs are equivalent.Ch. 5 - Find an Euler path if possible, and (b) find an...Ch. 5 - Find an Euler path if possible, and (b) find an...Ch. 5 - Find an Euler path if possible, and (b) find an...Ch. 5 - Find an Euler path if possible, and (b) find an...Ch. 5 - Parks The figure shows an arrangement of bridges...Ch. 5 - Architecture The floor plan of a sculpture gallery...Ch. 5 - Use Dirac's theorem to verify that the graph is...Ch. 5 - Use Dirac's theorem to verify that the graph is...Ch. 5 - Travel The table below lists cities serviced by a...Ch. 5 - Travel For the direct flights given in Exercise...Ch. 5 - Use the greedy algorithm to find a Hamiltonian...Ch. 5 - Use the greedy algorithm to find a Hamiltonian...Ch. 5 - Use the edge-picking algorithm to find a...Ch. 5 - Use the edge-picking algorithm to find a...Ch. 5 - Efficient Route The distances, in miles, between...Ch. 5 - Computer Networking A small office needs to...Ch. 5 - Show that the graphs is planar by finding a planar...Ch. 5 - Show that the graphs is planar by finding a planar...Ch. 5 - Show that the graph is not planar.Ch. 5 - Show that the graph is not planar.Ch. 5 - Count the number of vertices, edges, and faces in...Ch. 5 - Count the number of vertices, edges, and faces in...Ch. 5 - Map Coloring, a fictional map is given showing the...Ch. 5 - Map Coloring, a fictional map is given showing the...Ch. 5 - Show that the graph is 2-colorable by finding a...Ch. 5 - Show that the graph is 2-colorable by finding a...Ch. 5 - Determine (by trial and error) the chromatic...Ch. 5 - Determine (by trial and error) the chromatic...Ch. 5 - Scheduling A company has scheduled a retreat at a...Ch. 5 - Social Network Each vertex in the graph at the...Ch. 5 - Determine whether the following two graphs are...Ch. 5 - Answer the following questions for the graph shown...Ch. 5 - Recreation The illustration below depicts bridges...Ch. 5 - a. What does Dirac's theorem state? Explain how it...Ch. 5 - Low-Cost Route The table below shows the cost of...Ch. 5 - Use the greedy algorithm to find a Hamiltonian...Ch. 5 - Sketch a planar drawing of the graph below. Show...Ch. 5 - Answer the following questions for the graph shown...Ch. 5 - Map Coloring A fictional map of the countries of a...Ch. 5 - For the graph shown below, find a 2-coloring of...Ch. 5 - A group of eight friends is planning a vacation in...

Find more solutions based on key concepts

Show solutions Evaluate the expression sin Exercises 116. 23

Finite Mathematics

In problems 23-58, perform the indicated operations and simplify.
28.

Mathematical Applications for the Management, Life, and Social Sciences

Evaluate the integral. 2. 12x(x+1)2dx

Calculus: Early Transcendentals

In Exercises 6372, evaluate the expression. 67. 32+33

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

For Problems 29-32, classify the real number by tracing through the diagram in the text see page 16. Objective ...

Intermediate Algebra

Use a random-number table or random-number generator to simulate tossing a fair coin 10 times. Generate 20 such...

Understanding Basic Statistics

Magnitude of a Vector Find the magnitude of the given vector. 14. 1,6,22

Precalculus: Mathematics for Calculus (Standalone Book)

Specimens of three different types of rope wire were selected, and the fatigue limit (MPa) was determined for e...

Probability and Statistics for Engineering and the Sciences

In words, explain what is measured by SS, variance, and standard deviation.

Statistics for The Behavioral Sciences (MindTap Course List)

PA A random sample of 100 inmates at a maximum security prison shows that exactly 10 of the respondents had bee...

Essentials Of Statistics

Evaluate the expression and write your answer in the form a + bi. 13. 25

Multivariable Calculus

When measuring height to the nearest half inch, what are the real limits for a score of 69.0 inches? a. 68 and ...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Demand and Profit To generate a profit from its o'Books e-book service, OHaganBooks.com needs to know how the d...

Finite Mathematics and Applied Calculus (MindTap Course List)

Find the limit. 35. lims164ss16

Single Variable Calculus

Draw a contour map of the function showing several level curves. f(x,y)=x2y23

Calculus (MindTap Course List)

Finding Limits In Exercises 37-58, find the limit (if it exists). See Examples 5, 6, 7, 9, and 11. limt0(t+t)2-...

Calculus: An Applied Approach (MindTap Course List)

Finding and Analyzing Derivatives Using Technology In Exercises 63-70, (a) use a computer algebra system to dif...

Calculus: Early Transcendental Functions

Find the remaining trigonometric ratios. 33. cot = 3, 2

Single Variable Calculus: Early Transcendentals, Volume I

Add the following hexadecimal numbers. Check using decimals. 22+78

Elementary Technical Mathematics

For Questions 1 through 12, fill in each blank with the appropriate word, number, or equation. If y=tan1x, then...

Trigonometry (MindTap Course List)

19. Let be a subgroup of the group . Prove that for all right cosets and of in if and only if is normal ...

Elements Of Modern Algebra

6. When adding or subtracting decimals, we work from ________ to ________. (3-3)

Contemporary Mathematics for Business & Consumers

(a) What does lHospitals Rule say? (b) How can you use lHospitals Rule if you have a product f(x) g(x) where f(...

Single Variable Calculus: Early Transcendentals

In square ABCD not shown, point E lies on side DC. If AB=8 and AE=10, find BE.

Elementary Geometry For College Students, 7e

Let A and B be two events in a sample space S such that P(A)=.6, P(B)=.5, and P(AB)=.2. Find: a. P(AB)b. P(BA)

Finite Mathematics for the Managerial, Life, and Social Sciences

Evaluating an Improper Integral In Exercises 33-48, determine whether the improper integraldiverges or converge...

Calculus: Early Transcendental Functions (MindTap Course List)

Given: and intersect Prove: at ;

Elementary Geometry for College Students

Finding the Standard Equation of a Hyperbola In Exercises 21-24, find the standard form of the equation of the ...

Calculus of a Single Variable

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this u...

Mathematics For Machine Technology

Define primary and secondary sources and explain how each plays a role in the process of finding a research ide...

Research Methods for the Behavioral Sciences (MindTap Course List)

The paper referenced in the previous exercise also included data for a second radiologist, Radiologist 2. Based...

Introduction To Statistics And Data Analysis

True or False:
i + j is a unit vector in the direction of 5i + 5j.

Study Guide for Stewart's Multivariable Calculus, 8th

True or False: n=21(lnn)n converges.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Proof Prove that if f has an inverse function, then (f1)1=f

Calculus (MindTap Course List)

Laplaces EquationIn Exercises 9598, show that the function satisfies Laplaces equation 2z/x2+2z/y2=0. z=exsiny

Multivariable Calculus

Describe the limitations of counterbalancing and explain why partial counterbalancing is sometimes used.

Research Methods for the Behavioral Sciences (MindTap Course List)

A 95% confidence interval for a population mean was reported to be 152 to 160. If = 15, what sample size was u...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Use the graphs of functions f and g to answer each problem. ff-2

College Algebra (MindTap Course List)

An average of 15 aircraft accidents occur each year (The World Almanac and Book of Facts, 2004). a. Compute the...

Statistics for Business & Economics, Revised (MindTap Course List)

In Problems 126 solve the given differential equation by undetermined coefficients. 2. 4y + 9y = 15

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

Use the formula for the sum of the first n integers and/or the formula for the sum of a geometric sequence to e...

Discrete Mathematics With Applications

Exercises 5-12 use the FedEx travel times shown in Figure 9.56. Exercises 9-12 involve deliveries to City Hall,...

Mathematics: A Practical Odyssey

College Basketball Coachesâ€™ Salaries. In 2018, Mike Krzyewski and John Calipari topped the list of highest-paid...

Essentials Of Statistics For Business & Economics

Poker Hand You are dealt five cards from a standard deck of 52 playing cards. In how many ways can you get (a) ...

College Algebra

Reminder Round all answers to two decimal places unless otherwise indicated. Magnitude and EnergyThe magnitude ...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Headphones Conclusion. In exercise 18, the data on price ($) and the overall score for six stereo headphones te...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)