BuyFind*arrow_forward*

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.2, Problem 1EE

Textbook Problem

4 views

Continue investigating Hamiltonian circuits in Figure 5.12 by using the greedy algorithm starting at vertices C, D, and E. Then compare the various Hamiltonian circuits to identify the one with the smallest total weight.

To determine

The Hamiltonian circuits using greedy algorithm starting at vertices C, D and E. Then compare the various Hamiltonian circuits to identify the one with the smallest total weight.

**Calculation:**

The graph of Hamiltonian circuit is

Using Greedy algorithm, the Hamiltonian algorithm starting at vertices C is:

- Start at C, travel along the smallest weight edges, continue this until travel all vertices.
- Start at D, travel along the smallest weight edges, continue this until travel all vertices...

Therefore the Hamiltonian circuit is C − A − B − E − D − C.

Total weight of this circuit is 3 + 5 + 1 + 2 + 7 = 18

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 Let a=log2,b=log3, and c=log7. In Exercises 2946, use the logarithm identities to express the given quantity in...

Finite Mathematics

In Problems 61-68, perform the indicated operations with expressions involving fractional exponents and radical...

Mathematical Applications for the Management, Life, and Social Sciences

Marketing: Bargain Hunters In a marketing survey, a random sample of 1001 supermarket shoppers revealed that 27...

Understanding Basic Statistics

A sample of n = 5 scores has a mean of M = 12. If one new score with a value of X 18 is added to the sample, t...

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

Estimating Limits In Exercises 71-74, use a graphing utility to estimate the limit (if it exists). limx24x3+7x2...

Calculus: An Applied Approach (MindTap Course List)

Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find (app...

Calculus: Early Transcendentals

Solving Inequalities Solve the inequality. 82. x2ex 2ex 0

Precalculus: Mathematics for Calculus (Standalone Book)

A faucet is filling a hemispherical basin of diameter 60 cm with water at a rate of 2 L/min. Find the rate at w...

Single Variable Calculus: Early Transcendentals, Volume I

By any method, determine all possible real solutions of each equation in Exercises 1330. Check your answers by ...

Finite Mathematics and Applied Calculus (MindTap Course List)

Finding a Geometric Power Series In Exercises 93 and 94, find a geometric power series for the function, center...

Calculus: Early Transcendental Functions

Determine z for the following values of : a. = .0055 b. = .09 c. = .663

Probability and Statistics for Engineering and the Sciences

For each set of sample outcomes below, use Formula 6.2 to construct the 95 confidence interval for estimating ,...

Essentials Of Statistics

The curves with equations x = a sin nt, y = b cos t are called Lissajous figures. Investigate how these curves ...

Multivariable Calculus

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. Objectives 2 2a3a+7...

Intermediate Algebra

In Exercises 3148, (a) factor the given expression, and (b) set the expression equal to zero and solve for the ...

Applied Calculus

In a study examining the effect of alcohol on reaction time, Liguori and Robinson (2001) found that even modera...

Statistics for The Behavioral Sciences (MindTap Course List)

Determine whether the series is convergent or divergent. n=1nn3+1

Calculus (MindTap Course List)

In Exercises 13-20, sketch a set of coordinate axes and plot each point. 17. (8,72)

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

Find the limit, if it exists. If the limit does not exist, explain why. 43. limx0.52x12x3x2

Single Variable Calculus

Give the number of significant digits (the accuracy) of each measurement: 0.0070 W

Elementary Technical Mathematics

Evaluate the integral. 16. tan2xcos3xdx

Single Variable Calculus: Early Transcendentals

For Figure a of Exercise 1, find the number of faces, vertices, and edges in the polyhedron. Then verify Eulers...

Elementary Geometry For College Students, 7e

9. Consider the octic group of Example 3.
Find a subgroup of that has order and is a normal subgroup of .
Fi...

Elements Of Modern Algebra

As an insurance agent, calculate the annual premium for the following clients. Name Territory DriverClass Bodil...

Contemporary Mathematics for Business & Consumers

Distance In Figure 18, a person standing at point A notices that the angle of elevation to the top of the anten...

Trigonometry (MindTap Course List)

Commuter Trends: In a large metropolitan area, 20 of the commuters currently use the public transportation syst...

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding an Indefinite Integral In Exercises 15-34, find the indefinite integral. (Note: Solve by the simplest m...

Calculus of a Single Variable

Writing a Vector in Different Forms In Exercises 13and 14, the initial and terminal points of a vector are give...

Calculus: Early Transcendental Functions (MindTap Course List)

Use the Distance Formula to determine the type of triangle that has these vertices: a A0, 0,B4,0, and C2,5 b D0...

Elementary Geometry for College Students

Find length x. All dimensions are in millimeters

Mathematics For Machine Technology

Explain the issue of interdependence and independence of factors, and how it is related to interaction.

Research Methods for the Behavioral Sciences (MindTap Course List)

Write an iterated integral for the area of that part of the plane z = x that is above the region D at the right...

Study Guide for Stewart's Multivariable Calculus, 8th

Although studies continue to show smoking leads to significant health problems, 20% ofadults in the United Stat...

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

AreaIn Exercises 1922, find the area of the parallelogram that has the given vectors as adjacent sides. Use a c...

Multivariable Calculus

Explain the advantages and disadvantages of a stratified random sample compared with a proportionate stratified...

Research Methods for the Behavioral Sciences (MindTap Course List)

sec1(23)= a) 3 b) 3 c) 6 d) 6

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

Change each rational equation to quadratic form and solve it by the most efficient method. x+1=12x

College Algebra (MindTap Course List)

Graphing a Polar Equation In Exercises 45-54, use a graphing utility to graph the polar equation. Find an inter...

Calculus (MindTap Course List)

The article Report: More Than Half of DC-Area Millennials Are Using Ride-Hailing Apps (washingtonian.com/2016/0...

Introduction To Statistics And Data Analysis

The Commerce Department reported receiving the following applications for the Malcolm Baldrige National Quality...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

A statement of from xD , Q(x) is true if, and only if, Q(x) is ______ for ________.

Discrete Mathematics With Applications

From a 12inch-by-18inch piece of cardboard, 2-inch-square corners are cut out as shown in Figure 8.196, and the...

Mathematics: A Practical Odyssey

Market Demand This is a continuation of Exercise 13. The following table shows the quantity D of wheat, in bill...

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

Fill in the blanks. The equation (xh)2+(yk)2=r2 is the standard form of the equation of a with center and rad...

College Algebra

eICU Waiting Times. There is a severe shortage of critical care doctors and nurses to provide intensive-care se...

Essentials Of Statistics For Business & Economics