BuyFind*arrow_forward*

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.2, Problem 12ES

Textbook Problem

2 views

Use the greedy algorithm to find a Hamiltonian circuit starting at vertex A in the weighted

To determine

To determine a Hamiltonian circuit starting at vertex A in the weighted graph using the greedy algorithm.

**Given information:**

Given, weighted graph is:

â€ƒâ€ƒ

**Calculation:**

A path in a Hamiltonian graph is said to be a Hamiltonian Circuit if it begins and ends at the same vertex and passes through each vertex of a graph exactly once.

The greedy algorithm states to travel along a connected edge that has the smallest weight that is not yet visited. This process continues till all the vertices are visited and returned to the starting vertex.

Here, the vertex A is selected.

Vertex A is of degree 5 and the weights of the connected edges are 18, 16, 9, 17, 14

Hence, as per the Greedy Algorithm the edge with weight 9 is selected i.e. path reaches D.

Vertex D is of degree 5 and the weights of the connected edges are 25, 21, 9, 6, 12

Hence, as per the Greedy Algorithm the edge with weight 6 is selected i.e. path reaches F.

Vertex F is of degree 5 and the weights of the connected edges are 14, 16, 4, 6, 26

Hence, as per the Greedy Algorithm the edge with weight 4 is selected i.e. path reaches C.

Vertex C is of degree 5 and the weights of the connected edges are 5, 16, 4, 20, 25

The least of the weights is 4 but it leads to vertex F which is already visited...

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 CHECK POINT Decide which of the following are undefined.
1.

Mathematical Applications for the Management, Life, and Social Sciences

Rewrite each expression in Exercises 116 as a single rational expression, simplified as much as possible. 2x3x2...

Finite Mathematics

Describe the homogeneity of variance assumption and explain why it is important for the independent- measures t...

Statistics for The Behavioral Sciences (MindTap Course List)

Water is flowing at a constant rate into a spherical tank. Let V(t) be the volume of water in the tank and H(t)...

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 1-4, use the graph of the function f to find approximations of the given values. a. f(1) b. f(0) c...

Finite Mathematics and Applied Calculus (MindTap Course List)

The Augmented Matrix Write the augmented matrix for the system of linear equations. 11. {3x+yz=22xy=1xz=3

Precalculus: Mathematics for Calculus (Standalone Book)

Statistical Literacy When using the least-squares line for prediction, are results usually more reliable for ex...

Understanding Basic Statistics

Show that a projectile reaches three-quarters of its maximum height in half the time needed to reach its maximu...

Multivariable Calculus

Determine whether the differential equation is linear. 3. uet=t+tdudt

Calculus: Early Transcendentals

Statistical methods arc classified into two major categories: descriptive and inferential. Describe the general...

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

Even and Odd Functions and Zeros of Functions In Exercises 75-78, determine whether the function is even, odd, ...

Calculus: Early Transcendental Functions

Calculate each expression in Exercises 124, giving the answer as a whole number or a fraction in lowest terms. ...

Applied Calculus

The Shannon index sometimes called the Shannon-Wiener index or Shannon-Weaver index is a measure of diversity i...

Calculus (MindTap Course List)

The following table presents the annual person-hours of time lost due to traffic congestion for a group of citi...

Essentials Of Statistics

Translate the English phrase four subtracted from three times a number into an algebraic expression.

Intermediate Algebra

Fill in the blanks. 11. a. If f and g are continuous at a, then f g and fg are continuous at ________. Also, f...

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

Finding Slopes of Lines In Exercises 53-56, find the slope of the line passing through the pair of points. (5,2...

Calculus: An Applied Approach (MindTap Course List)

Evaluate the difference quotient for the given function. Simplify your answer. 27. f(x) = 4 + 3x x2, f(3+h)f(3...

Single Variable Calculus

The Pew Forum on Religion and Public Life reported on Dec. 9, 2009, that in a survey of 2003 American adults, 2...

Probability and Statistics for Engineering and the Sciences

Use the scale drawing of a metal plate cover in Illustration 2 in Exercises 1726: ILLUSTRATION 2 What are the d...

Elementary Technical Mathematics

Calculate the missing Information for the following taxpayers. Filing Status Adjustment Adjusted Gross (circle ...

Contemporary Mathematics for Business & Consumers

23. Let where . Prove .

Elements Of Modern Algebra

Find the number n such that i=1ni=78.

Single Variable Calculus: Early Transcendentals

Given: ABC with medians AE,CD,BF Find: a BG if BF=18 b GE if AG=4 c DG if CG=43

Elementary Geometry For College Students, 7e

If cosA=13 and A is between 90 and 180, find cos 2A

Trigonometry (MindTap Course List)

QUALITY CONTROL Copykwik has four photocopy machines: A, B, C, and D. The probability that a given machine will...

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding or Evaluating an Integral In Exercises 5360, find or evaluate the integral. sin32cosd

Calculus: Early Transcendental Functions (MindTap Course List)

Sketching a Graph by Point Plotting In Exercises 7-16, sketch the graph of the equation by point plotting. y=4x...

Calculus of a Single Variable

For Exercises 1 to 8, use the accompanying drawing. If VUVT and mT=72, find mV.

Elementary Geometry for College Students

A special washer-faced nut is shown in Figure 4-5. All dimensions are in inches. a. Determine the distance acro...

Mathematics For Machine Technology

A hot tub manufacturer advertises that with its heating equipment, a temperature of 100Fcan be achieved on aver...

Introduction To Statistics And Data Analysis

True or False:
is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th

A study investigated the relationship between audit delay (Delay), the length of time from a companys fiscal ye...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Search in a current newspaper or on a news website and find one news story that is based on the results of a re...

Research Methods for the Behavioral Sciences (MindTap Course List)

Finding Partial Derivatives In Exercises 11-40, find both first partial derivatives. z=coshxy2

Multivariable Calculus

Write each expression without absolute value symbols. |12|

College Algebra (MindTap Course List)

Finding an Equation of a Tangent Line In Exercises 29-36, (a) find an equation of the tangent line to the graph...

Calculus (MindTap Course List)

The following were collected for the Master Blend Coffee production process. The data show the filling weights ...

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

Describe the difference between inductive and deductive reasoning and give an example of each.

Research Methods for the Behavioral Sciences (MindTap Course List)

limx6(x210x)=. a) 24 b) 6 c) 26 d) does not exist

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

Write each of 43-52 using summation or product notation. (131)(231)+(331)(431)+(531)

Discrete Mathematics With Applications

37.Tourism sales. Figure 11.6 gives the total sales in the United States for two tourism-related industries: ho...

Mathematics: A Practical Odyssey

Three large tanks contain brine, as shown in Figure 3.3.8. Use the information in the figure to construct a mat...

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

50. A telephone survey to determine viewer response to a new television show obtained the following data.
Ratin...

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

Coupon Usage. Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. They are ...

Essentials Of Statistics For Business & Economics

Reminder Round all answers two decimals places unless otherwise indicated. The Sonora Pass California State Hig...

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