Business
Engineering
Math
Science
Social Science
Route Planning A security officer patrolling a city neighborhood needs to drive every street each night. The officer has drawn a graph to represent the neighborhood in which the edges represent the streets and the vertices correspond to street intersections. Would the most efficient way to drive the streets correspond to an Euler circuit, a Hamiltonian circuit, or neither? (The officer must return to the starting location when finished.) Explain your answer.
BuyFindarrow_forward
Mathematical Excursions (MindTap C...
4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Solutions
Chapter
Section
BuyFindarrow_forward
Mathematical Excursions (MindTap C...
4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 5.2, Problem 31ES
Textbook Problem
40 views
Route Planning A security officer patrolling a city neighborhood needs to drive every street each night. The officer has drawn a graph to represent the neighborhood in which the edges represent the streets and the vertices correspond to street intersections. Would the most efficient way to drive the streets correspond to an Euler circuit, a Hamiltonian circuit, or neither? (The officer must return to the starting location when finished.) Explain your answer.
To determine
To find if the most efficient way to drive the streets correspond to an Euler circuit, a Hamiltonian circuit, or neither.
Explanation of Solution
Given information:
Given, a security officer patrolling a city neighborhood needs to drive every street each night.
The officer has drawn a graph to represent the neighborhood in which the edges represent the streets and the vertices correspond to street intersections.
The officer must return to the starting location when finished.
Calculation:
A circuit (that starts and ends at the same vertex) is said to be an Euler circuit if it uses every edge but only once. (i.e...
Chapter 5 Solutions
Mathematical Excursions (MindTap Course List)
Show all chapter solutions
addCh. 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...
Additional Math Textbook Solutions
Find more solutions based on key concepts
Show solutions addIn Problems 27-30, the demand functions for and units of two related products, A and B, are given. Complete p...
Mathematical Applications for the Management, Life, and Social Sciences
Evaluate expressions in Exercises 3756, rounding your answer to four significant digits where necessary. 8643
Finite Mathematics
For Problems 96-104, write a numerical statement to represent the problem. Then simplify the numerical expressi...
Intermediate Algebra
Finding a Taylor PolynomialIn Exercises 27-32, find the n th Taylor polynomial for the function, centered at c....
Calculus: Early Transcendental Functions
Agriculture: Cotton A botanist has developed a new hybrid cotton plant that can withstand insects better than o...
Understanding Basic Statistics
If A and B are independent events, show that A and B are also independent. [Hint: First establish a relationshi...
Probability and Statistics for Engineering and the Sciences
Find the derivative. Simplify where possible. 43. y=xsinh(x/3)9+x2
Single Variable Calculus: Early Transcendentals, Volume I
Find the radius of convergence and interval of convergence of the series. n=1n!xn135(2n1)
Calculus (MindTap Course List)
Using Parentheses when Differentiating In Exercises 25-30, find the derivative of the function. See Example 6. ...
Calculus: An Applied Approach (MindTap Course List)
For the function A whose graph is shown, state the following. (a) limx3A(x) (b) limx2A(x) (c) limx2+A(x)` (d) l...
Single Variable Calculus
In Exercises 75-98, perform the indicated operations and/or simplify each expression. 93. (2x2 1)(3x2) + (x2 +...
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
A sample of n = 8 scores has a mean of M = 12. What is the value of EX for this sample?
Statistics for The Behavioral Sciences (MindTap Course List)
A researcher is interested in the texting habits of high school students in the United States. The researcher s...
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Use the Integral Test to determine whether the series is convergent or divergent. 8. n=1n2en3
Multivariable Calculus
Planting Crops A farmer has 300 acres of arable land on which she wants to plant cauliflower and cabbage. The f...
Precalculus: Mathematics for Calculus (Standalone Book)
Simplify the expressions in Exercises 5764, given that x,y,z,a,b, and c are positive real numbers. a2b2
Finite Mathematics and Applied Calculus (MindTap Course List)
Following are brief descriptions of how researchers measured a variable. For each situation, determine the leve...
Essentials Of Statistics
Find the lengths of the sides of the triangle PQR. Is it a right triangle? Is it an isosceles triangle? 9. P(3....
Calculus: Early Transcendentals
Factor completely: 5y2+11y+2
Elementary Technical Mathematics
George Bell bought an ultralight airplane for $29,200. He made a 15 down payment and financed the balance with ...
Contemporary Mathematics for Business & Consumers
Draw the vector V that goes from the origin to the given point. Then write V in component form a,b . (5,5)
Trigonometry (MindTap Course List)
Given that CF is a tangent to the circle shown: a)mAB=80,mAEB=75,mCD=?b)mAC=62,mDEB=45,mBD=?c)mAB=88,mP=24,mCED...
Elementary Geometry For College Students, 7e
Write and as given in Exercises, find the and that satisfy the condition in a Division Algorithm.
...
Elements Of Modern Algebra
Use the guidelines of this section to sketch the curve. y = x3 + 3x2
Single Variable Calculus: Early Transcendentals
COMMUTER TRENDS Within a large metropolitan area, 20 of the commuters currently use the public transportation s...
Finite Mathematics for the Managerial, Life, and Social Sciences
Finding a Derivative In Exercises 57-82, find the derivative of the function. f(s)=(s21)5/2(s3+5)
Calculus: Early Transcendental Functions (MindTap Course List)
For ABC and DEF not shown, suppose that ACDF, ABDE and mAmD. Draw a conclusion regarding the length of BC and E...
Elementary Geometry for College Students
Finding a Derivative In Exercises 43-66, find the derivative of the function. f(x)=ln(x2+3)
Calculus of a Single Variable
Express the following decimal numbers as binary numbers. 101.25
Mathematics For Machine Technology
FindingTangentialand NormalComponents of Acceleration In Exercises 25-30, Find the tangential and normal compon...
Calculus (MindTap Course List)
If A and B are 22 matrices, is (AB)2 equal to A2B2? Support your answer.
College Algebra (MindTap Course List)
Finding Volume In Exercises 21-26, use a double integral to find the volume of the indicated solid.
Multivariable Calculus
Nielsen Media Research identified Empire and the Big Bang theory as the two top-rated prime-time television ser...
STATISTICS F/BUSINESS+ECONOMICS-TEXT
The interval of convergence of is:
[−1, 1]
[−1, 1)
(−1, 1]
(−1, 1)
Study Guide for Stewart's Multivariable Calculus, 8th
In addition to the key words, you should also be able to define the following terms: Statistical significance. ...
Research Methods for the Behavioral Sciences (MindTap Course List)
What is the number of the integral formula in your texts Table of Integrals that may be used to evaluate x2+2x+...
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Identify possible sources and use them to identify a topic area for research.
Research Methods for the Behavioral Sciences (MindTap Course List)
A tennis shop sells five different brands of rackets, each of which comes in either a midsize version or an ove...
Introduction To Statistics And Data Analysis
Consumer Reports provided overall customer satisfaction scores for ATT, Sprint, T-Mobile, and Verizon cell-phon...
Statistics for Business & Economics, Revised (MindTap Course List)
Exercises 1-5 contains a while loop and a predicate. In each case show that if the predicate is true before ent...
Discrete Mathematics With Applications
In Problems 122 solve the given differential equation by separation of variables. 3. dx+e3xdy=0
A First Course in Differential Equations with Modeling Applications (MindTap Course List)
James Magee is thinking of buying a home for 124,500. Bank of the Future advertises an 80, thirty-year simple i...
Mathematics: A Practical Odyssey
31. Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = .3...
Essentials Of Statistics For Business & Economics
9. In a recent poll six hundred adults were asked a series of questions about the state of the economy and thei...
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
Round each percentage increase or decrease that you calculate to nearest tenth of a percent. Percentage Change ...
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
