BuyFind*arrow_forward*

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.1, Problem 5ES

Textbook Problem

16 views

Determine (a) the number of edges in the graph, (b) the number of vertices in the graph, (c) the number of vertices that are of odd degree, (d) whether the graph is connected, and (e) whether the graph is a complete graph.

To determine

**(a)**

To determine the number of edges in the graph.

**Given information:**

Given graph is

â€ƒâ€ƒ

To determine

**(b)**

To determine the number of vertices in the graph.

To determine

**(c)**

To determine the number of vertices that are of odd degree.

To determine

**(d)**

To determine whether the graph is connected.

To determine

**(e)**

To determine whether the graph is a complete graph.

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

Finite Mathematics

72.Advertising and sales Suppose it has been determined that the sales at Ewing Gallery decline after the end o...

Mathematical Applications for the Management, Life, and Social Sciences

Sketch the graphs of the equations in Exercises 512. 2y+x=1

Applied Calculus

For any events A and B with P(B) 0, show that P(A|B) + P(A|B) = 1.

Probability and Statistics for Engineering and the Sciences

Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t)=costi+3tj+2sin2tk,...

Calculus (MindTap Course List)

For Problems 1-50, solve each equation. Objective 1 5x+1=14

Intermediate Algebra

Finding the Least Squares Regression Quadratic In Exercises 33-36, use the result of Exercise 31 to find the le...

Calculus: Early Transcendental Functions

(a) Use a graph to find a number such that if4x4+thenx2+4x4100 (b) What limit does part (a) suggest is true?

Single Variable Calculus

Determining Continuity In Exercises 11-40, describe the interval(s) on which the function is continuous. Explai...

Calculus: An Applied Approach (MindTap Course List)

Simplify each expression in Exercises 1730, expressing your answer in positive exponent form. xy1x1

Finite Mathematics and Applied Calculus (MindTap Course List)

Logarithmic Form Express the equation in logarithmic form. 21. (a) 4x = 70 (b) 35 = w

Precalculus: Mathematics for Calculus (Standalone Book)

Find a formula for the described function and state its domain. 58. A rectangle has area 16 m2. Express the per...

Single Variable Calculus: Early Transcendentals, Volume I

Profits: Retail Jobs and productivity! How do retail stores rate? One way to answer this question is to examine...

Understanding Basic Statistics

Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate i...

Calculus: Early Transcendentals

For the following population of N=6 scores 9,6,8,9,8 a. Calculate the range and the standard deviation. (Use ei...

Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 79-84,determine whether the statement is true or false for all real numbers a and b. 80. |b2| = b2

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

SOC Nationally, the per capita monthly fuel oil bill is 110. A random sample of 36 cities in the South-east ave...

Essentials Of Statistics

The results of a recent study showed that children who routinely drank reduced fat milk (1% or skim) were more ...

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

Determine whether the series is convergent or divergent. 15. n=21nlnn

Multivariable Calculus

Factor each trinomial completely: 2a218a+28

Elementary Technical Mathematics

Graph one complete cycle for each of the following. In each case, label the axes accurately and state the perio...

Trigonometry (MindTap Course List)

A sector with perimeter 30 in. has a bounding arc of length 12 in. Find the length of the radius of the circle.

Elementary Geometry For College Students, 7e

Find f. f(x) = x3 + sinh x, f(0) = 1, f(2) = 2.6

Single Variable Calculus: Early Transcendentals

Read and write the following whole numbers in numerical and word form.
Number Numerical Form Word Form
2. ...

Contemporary Mathematics for Business & Consumers

True or False
Label each of the following statements as either true or false.
7. for all and in .

Elements Of Modern Algebra

In Exercises 11-18, write a system of linear inequalities that describes the shaded region.

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding the Domain In Exercises 41-46, find the domain of the function. f(x)=12ex

Calculus: Early Transcendental Functions (MindTap Course List)

Determining Concavity In Exercises 43-48, determine the open t-intervals on which the curve is concave downward...

Calculus of a Single Variable

Given: 1 is complementary to 2; 2 is complementary to 3 Prove: BDAE

Elementary Geometry for College Students

Identify the angle that corresponds with A, D, and ACB.

Mathematics For Machine Technology

for the 20102011 viewing season, the top five syndicated programs were wheel of Fortune (WoF), Two and Half Men...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Consider the following hypothesis test: H0: p .75 Ha: p .75 A sample of 300 items was selected. Compute the p...

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

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)

The point plotted at the right has coordinates:
(2, 5, 4)
(5, 2, 4)
(4, 2, 5)
(2, 4, 5)

Study Guide for Stewart's Multivariable Calculus, 8th

Projectile Motion The position of a baseball. is represented by r(t)=502ti+(3+502t16t2)j. Find the arc length o...

Calculus (MindTap Course List)

Suppose that 30% of all automobiles undergoing an emissions inspection at an inspection station fail the inspec...

Introduction To Statistics And Data Analysis

CurvatureVerify that the curvature at any point (x,y) on the graph of y=coshx is 1/y2.

Multivariable Calculus

Determine whether each function is even, odd, or neither.

College Algebra (MindTap Course List)

Describe how the third-variable problem and the directionality problem limit the interpretation of results from...

Research Methods for the Behavioral Sciences (MindTap Course List)

A definite integral for the area under the curve described by x = t2 + 1, y = 2t, 0 t 1 is: a) 01(2t3+2t)dt b...

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

(a) Give a convincing demonstration that the second-order equation ay + by + cy = 0, a, b, and c constants, alw...

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

Use truth tables to establish the truth of each statement in 24-27. A conditional statement is not logically eq...

Discrete Mathematics With Applications

In Exercises 27-56, use a calculator to find each value. Give the entire display of your calculator. a. e4.5101...

Mathematics: A Practical Odyssey

The Single-Graph Method In Exercises S-17 through S-28, use the single-graph method to solve the given equation...

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

8. Refer to the NCP data in Table 13.4. Set up the ANOVA table and test for any significant difference in the m...

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

Unemployment in Older Workers.â€ƒOlder people often have a hard time finding work. AARP reported on the number of...

Essentials Of Statistics For Business & Economics