BuyFind*arrow_forward*

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.1, Problem 27ES

Textbook Problem

880 views

Pets The diagram below shows the arrangement of a Habitrail cage for a pet hamster. (Plastic tubes connect different cages.) Is it possible for a hamster to travel through every tube without going through the same tube twice? If so, find a route for the hamster to follow. Can the hamster return to its starting point without repeating any tube passages?

To determine

To determine if it is possible for a hamster to travel through every tube without going through the same tube twice. And if it can, to find the route for the hamster to follow. To check if the hamster can return to its starting point without repeating any tube passages.

**Given information:**

Given, the diagram below shows the arrangement of a Habitrail cage for a pet hamster. (Plastic tubes connect different cages.)

â€ƒâ€ƒ

**Calculation:**

To check the possibility of the travel, the arrangement is to be graphed.

Every cage is considered as a vertex and every pipe is considered an edge.

Also, there are two intersections of pipe where there is no cage but are to be considered vertices as that part of pipe can be considered as another edge.

â€ƒâ€ƒ

Using the above image, the graph can be made as:

â€ƒâ€ƒ

It is possible for a hamster to travel through every tube without going through the same tube 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...

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 In problems 9-18, simplify the expressions with all exponents positive.
17.

Mathematical Applications for the Management, Life, and Social Sciences

Find the limit of the sequence {2,22,222,...}

Calculus: Early Transcendentals

Convert each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

Finite Mathematics and Applied Calculus (MindTap Course List)

Let X have a Poisson distribution with parameter . Show that E(X) = directly from the definition of expected v...

Probability and Statistics for Engineering and the Sciences

PA The city manager has received a complaint from the local union of firefighters to the effect that they are u...

Essentials Of Statistics

Find the exact trigonometric ratios for the angle whose radian measure is given. 23. 34

Single Variable Calculus: Early Transcendentals, Volume I

Find the limit. 32. limv4+4v4v

Single Variable Calculus

Limits and Continuity Sketch the graph of the function f(x)=[x]+[x]. (a) Evaluate f (1), f (0), f(12), and f(2....

Calculus: Early Transcendental Functions

Terminology Consider the graph of a normal probability distribution of x values with mean and standard deviati...

Understanding Basic Statistics

Concept Quiz 2.1 For Problems 1-10, answer true or false. If 5 is a solution, then a true numerical statement i...

Intermediate Algebra

In Exercises 63-68, rationalize the denominator. 68. 2xy

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

In Exercises 9-14, decide whether the specified values come from a linear, quadratic, exponential, or absolute ...

Applied Calculus

Expressing a Function as a Composition Express the function in the form f g. 66. G(x)=1x+3

Precalculus: Mathematics for Calculus (Standalone Book)

Place the following scores in a frequency distribution table. Based on the frequencies, what is the shape of th...

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

Sketching the Graph of an Equation In Exercises 7-22, sketch the graph of the equation. Use a graphing utility ...

Calculus: An Applied Approach (MindTap Course List)

Find the indicated partial derivative(s). 70. u = xaybzc; 6uxy2z3

Multivariable Calculus

Repeat Exercise 29 for the curve y=x+sinx 0x2

Calculus (MindTap Course List)

Find each value requested for the distribution of scores in the following table. X Y 5 1 4 3 3 4 2 5 1 2 n X X2

Statistics for The Behavioral Sciences (MindTap Course List)

Given the equation 3x4y=24, complete each ordered pair: (4,)

Elementary Technical Mathematics

Find the derivative of the function. F(t)=t2t3+1

Single Variable Calculus: Early Transcendentals

Solve the following for the portion, rate, or base, rounding decimals to hundredths and percents to the nearest...

Contemporary Mathematics for Business & Consumers

Note: Exercises preceded by an asterisk are of a more challenging nature. In Exercises 3 to 8, use the drawing ...

Elementary Geometry For College Students, 7e

Geometry: Characteristics of a Cube The object shown in Figure 27 is a cube (all edges are equal in length). Us...

Trigonometry (MindTap Course List)

Label each of the following statements as either true or false. 24.

Elements Of Modern Algebra

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

Finite Mathematics for the Managerial, Life, and Social Sciences

For quadrilateral ABCD,AC and BD are diagonals. Also, ABBD,ACCD, and CFBD. Give the reason why: a ABECFE b CFED...

Elementary Geometry for College Students

Verifying a Formula In Exercises 33-36, use the method of partial fractions to verify the integration formula. ...

Calculus: Early Transcendental Functions (MindTap Course List)

Writing In Exercises 5 and 6, consider the polar equation r=41+esin Use a graphing utility to graph the equatio...

Calculus of a Single Variable

Raise the following terms to indicated powers. (8C3FH2)2

Mathematics For Machine Technology

Sometimes, Always, or Never:
is the volume above the rectangular region R and under .

Study Guide for Stewart's Multivariable Calculus, 8th

Define primary and secondary sources, identity examples of each, and explain the role that each plays in a lite...

Research Methods for the Behavioral Sciences (MindTap Course List)

Changing the Order of Integration In Exercises 45-50. sketch the region R of integration and change the order o...

Multivariable Calculus

Construct a stem-and-leaf display for the following data. Use a leaf unit of 10. 1161 1206 1478 1300 1604 1725 ...

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

A chemical supply company currently has in stock 100 pounds of a certain chemical, which it sells to customers ...

Introduction To Statistics And Data Analysis

Think About It The figure shows the graphs of the functions y1=x,y2=12x3/2,y3=14x2,, and y4=18x5/2 on the inter...

Calculus (MindTap Course List)

Find all rational zeros of each polynomial function. P(x)=x38x2x+8

College Algebra (MindTap Course List)

With an initial estimate of âˆ’1, use Newtonâ€™s Method once to estimate a zero of f(x) = 5x2 + 15x + 9.

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

Define content analysis, and explain how it is different from regular behavioral observational.

Research Methods for the Behavioral Sciences (MindTap Course List)

Consider a Poisson distribution with a mean of two occurrences per time period. a. Write the appropriate Poisso...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Determine which statements in 6-16 are true and which are false, Prove those that are true and disprove those t...

Discrete Mathematics With Applications

A nationwide survey performed by Get Out of My Way magazine indicates that 31 of the bike owners who do not cur...

Mathematics: A Practical Odyssey

Consider the linear system X = AX of two differential equations, where A is a real coefficient matrix. What is ...

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

Increases in Customer Satisfaction. Will improving customer service result in higher stock prices for the compa...

Essentials Of Statistics For Business & Economics

34. Management proposed the following regression model to predict sales at a fast-food outlet.
y = Î²0 + Î²1x1 + ...

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

Finding Maxima and Minima In Exercises S-5 through S-23, find all maxima and minima as instructed. You should f...

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

In the following exercises, use the graph of function y=f(x) shown here to find the value, if possible. Estimat...

Calculus Volume 1