BuyFind*arrow_forward*

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.1, Problem 30ES

Textbook Problem

93 views

Architecture, a floor plan of a museum is shown. Draw a graph that represents the floor plan, where each vertex represents a room and an edge connects two vertices if there is a doorway between the two rooms. Is it possible to walk through the museum and pass through each doorway without going through any doorway twice? Does it depend on whether you return to the room you started at? Justify your conclusion.

To determine

To graph the floor plan. To determine if it is possible to walk through the museum and pass through each doorway without going through any doorway twice. To check if it depends on whether the ending point is same as the starting point.

**Given information:**

Given, a floor plan of a museum is shown below, in whose graph each room is represented by a vertex and a doorway between the two rooms is represented by an edge.

â€ƒâ€ƒ

**Calculation:**

To make the graph, the rooms are labelled first as per the given information.

â€ƒâ€ƒ

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

â€ƒâ€ƒ

It is possible to walk through the museum and pass through each doorway without going through any doorway 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 Evaluate the expression sin Exercises 116. (32)3

Finite Mathematics

71. Rental A rental truck costs for a day plus per mile.
If x is the number of miles driven, write an expressio...

Mathematical Applications for the Management, Life, and Social Sciences

Estimating Slope In Exercises 1-4, estimate the slope of the line.

Calculus: An Applied Approach (MindTap Course List)

Show that the function is continuous on its domain. State the domain. 47. h(x)=x4+x3cosx

Single Variable Calculus

For each of the following confidence levels, determine the corresponding Z score. Confidence Level Alpha Area B...

Essentials Of Statistics

In Exercises 69-74, rationalize the numerator. 71. 2yx

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

In a classic study in the area of problem solving, Katona (1940) compared the effectiveness of two methods of i...

Statistics for The Behavioral Sciences (MindTap Course List)

Terminology If it makes sense to say that one data measurement in a data set is twice that of another measureme...

Understanding Basic Statistics

For the following scores, the smallest value is X 7 and the largest value is X 48. a. Determine the best inte...

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

What is an increasing function?

Calculus (MindTap Course List)

The total fertility rate at time t, denoted by F(t), is an estimate of the average number of children born to e...

Calculus: Early Transcendentals

Solving an Equation In Exercises 11-26, solve for x. 343=(5x7)3

Calculus: Early Transcendental Functions

For Problems 51-66, use an algebraic approach to solve each problem. Objective 2 Find three consecutive integer...

Intermediate Algebra

A sample of 50 lenses used in eyeglasses yields a sample mean thickness of 3.05 mm and a sample standard deviat...

Probability and Statistics for Engineering and the Sciences

Solve the equations in Exercises 126. (x2+1)(x+1)43(x+1)73=0

Applied Calculus

A variable star is one whose brightness alternately increases and decreases. For the most visible variable star...

Single Variable Calculus: Early Transcendentals, Volume I

Rewrite each expression in Exercises 116 as a single rational expression, simplified as much as possible. 1x[x3...

Finite Mathematics and Applied Calculus (MindTap Course List)

Graphing Polynomials Factor the polynomial and use the factored form to find the zeros. Then sketch the graph. ...

Precalculus: Mathematics for Calculus (Standalone Book)

Use Lagrange multipliers to give an alternate solution to the indicated exercise in Section 14.7. 37. Exercise ...

Multivariable Calculus

Find angle A in Illustration 3. ILLUSTRATION 3

Elementary Technical Mathematics

Sketch the graph of the function. 47. g(t) = |1 3t|

Single Variable Calculus: Early Transcendentals

In Exercise 1 to 10, classify each statement as true or false. Because mA=mABC, it follows that DA=DC.

Elementary Geometry For College Students, 7e

The effective or true annual interest rate being charged for credit is known as the ______ ____ ______ and is a...

Contemporary Mathematics for Business & Consumers

Use your graphing calculator to graph each of the following between x=0 and x=4. In each case, show the graph o...

Trigonometry (MindTap Course List)

Solve each of the following equations by finding [ a ]1 and using the result in Exercise 9. a.[ 4 ][ x ]=[ 5 ]i...

Elements Of Modern Algebra

Give three characteristics of a standard minimization linear programming problem.

Finite Mathematics for the Managerial, Life, and Social Sciences

For exercises 42 to 44, O is the inscribed circle for ABC. In exercises 43 and 44, use the result from Exercise...

Elementary Geometry for College Students

The polar equations r=sin2,r=sin2, and r=sin(2) all have the same graph.

Calculus: Early Transcendental Functions (MindTap Course List)

Solving a First-Order Linear Differential Equation In Exercises 7-14, find the general solution of the first-or...

Calculus of a Single Variable

Express each of the following problems as an algebraic expression. The product of x and y divided by the square...

Mathematics For Machine Technology

Blackjack, or twenty-one as it is frequently called, is a popular gambling game played inLas Vegas casinos. A p...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Finding the Arc Length of a Polar Curve In Exercises 53-58, find the length of the curve over the given interva...

Calculus (MindTap Course List)

Surfing lessons Dylan and Dusty plan to take weekly surfing lessons together. If the 2-hour lessons are 40 per ...

College Algebra (MindTap Course List)

Describe the purpose and responsibilities of the Institutional Animal Care and Use Committee (IACUC).

Research Methods for the Behavioral Sciences (MindTap Course List)

As part of a study on transportation safety, the U.S. Department of Transportation collected data on the number...

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

Construct a frequency distribution histogram or polygon for the set of scores presented in the following freque...

Research Methods for the Behavioral Sciences (MindTap Course List)

The Knight Foundation asked each person in a representative sample of high school students and in a representat...

Introduction To Statistics And Data Analysis

is the binomial series for:

Study Guide for Stewart's Multivariable Calculus, 8th

Finding Partial DerivativesIn Exercises 1518, find w/s and w/t using the appropriate Chain Rule. Evaluate each ...

Multivariable Calculus

True or False:
By the Integral Test, converges.

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

In Problems 21-28 find the critical points and phase portrait of the given autonomous first-order differential ...

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

The formula 1+r+r2++rn=rn+11r1 is true for every real number r except r=1 and for every integer n0. Use this fa...

Discrete Mathematics With Applications

In Exercises 122, construct a Venn diagram to determine the validity of the given argument. 1. Some actors are ...

Mathematics: A Practical Odyssey

Finding the Domain of a Rational Function In Exercises 5-12, find the domain of the function and discuss the be...

College Algebra

Time Spent Channel Surfing.â€ƒAccording to Ericssonâ€™s 2016 ConsumerLab TV & Media report, the average person in t...

Essentials Of Statistics For Business & Economics

Graphs and Function values: Get the standard view of the graph of f=2x2. Use the graph to get the value of f(3)...

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

CASE PROBLEM 1: WENTWORTH MEDICAL CENTER As part of a long-term study of individuals 65 years of age or older, ...

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