BuyFind*arrow_forward*

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.3, Problem 29ES

Textbook Problem

1 views

Show that the complete graph with five vertices,

To determine

**To Prove:**

**Given information:**

A complete graph with 5 vertices,

**Formula used:**

__Euler's Formula: __v + f = c + 2, where f is the number of faces, v is the number of vertex and c is the number of edges.

**Calculation:**

The graph of

Number of vertices (v) = 5

Number of faces (f) = 12

Number of edges (c) = 10

Sub

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

Finite Mathematics

In Problems 33 â€“ 38, solve each inequality.
34.

Mathematical Applications for the Management, Life, and Social Sciences

Quadratic Equations Find all solutions of the equation and express them in the form a + bi. 70. t+3+3t=0

Precalculus: Mathematics for Calculus (Standalone Book)

Solve the equations in Exercises 126. (x2+1)x+1(x+1)3=0

Applied Calculus

Find all solutions of the equation. 20. x4 = 1

Multivariable Calculus

What is the last step in the calculation of (X)2? a. Square each score. b. Add the scores. c. Square the sum of...

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

(a) Prove that the equation has at least one real root. (b) Use your calculator to find an interval of length 0...

Single Variable Calculus

A random sample of n=12 individuals is selected from a population with =70 , and a treatment is administered to...

Statistics for The Behavioral Sciences (MindTap Course List)

a. The students at Littlewood Regional High School cut an average of 3.3 classes per month. A random sample of ...

Essentials Of Statistics

Finding Intercepts In Exercises 19-28, find any intercepts. y=x16x2

Calculus: Early Transcendental Functions

Finding an Equation of a Tangent Line In Exercises 45-48, (a) find an equation of the tangent line to the graph...

Calculus: An Applied Approach (MindTap Course List)

Use the Chain Rule to show that if is measured in degrees, then dd(sin)=180cos (This gives one reason for the ...

Single Variable Calculus: Early Transcendentals, Volume I

Let U have a uniform distribution on the interval [0, 1].Then observed values having this distribution can be o...

Probability and Statistics for Engineering and the Sciences

Alzheimers Disease The projected number of people aged 65 and over in the U.S. population with Alzheimers disea...

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

For Problems 3-11, simplify each numerical expression. 3(2)3+4(2)29(2)14

Intermediate Algebra

Trace or copy the graph of the function. Then sketch a graph of its derivative directly beneath.

Calculus: Early Transcendentals

Marketing: Age What is the age distribution of promotion-sensitive shoppers? A supermarket super shopper is def...

Understanding Basic Statistics

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)

Find a+b,4a+2b,|a|, and |ab|. a=3,4,b=9,1

Calculus (MindTap Course List)

Find the length of time each IV should be administered (assume a drop factor of 10 drops/mL): 1.4 L at a rate o...

Elementary Technical Mathematics

For the matrices in Exercise 12, evaluate (A+B)2 and A2+2AB+B2 and compare the results.

Elements Of Modern Algebra

Find the absolute maximum and absolute minimum values of f on the given interval. f(x)=x+1x,[0.2,4]

Single Variable Calculus: Early Transcendentals

The percent markup based on selling price is equal to the divided by the selling price. (8-5)

Contemporary Mathematics for Business & Consumers

In Exercise 23 to 30, determine the value of x so that line l will be parallel to line m. m1=x2+35 m5=3x4

Elementary Geometry For College Students, 7e

Convert 14.65 to degrees and minutes.

Trigonometry (MindTap Course List)

Fill in the blanks. An arrangement of a set of distinct objects in a definite order is called a/an ; an arrange...

Finite Mathematics for the Managerial, Life, and Social Sciences

Proof Prove that the tangent of the angle (0/2) between the radial line and the tangent line at the point (r,) ...

Calculus: Early Transcendental Functions (MindTap Course List)

Finding an Integral Using Technology In Exercises 7780, use a computer algebra system to find the integral. Use...

Calculus of a Single Variable

Consider the regular square pyramid shown. a Find the length of the slant height l correct to tenths. b Use l f...

Elementary Geometry for College Students

In exercise 7-10, determine the number of vertices, edges and loops in the given graph.

Mathematics: A Practical Odyssey

In each of 13-19,(a) rewrite the statement in English without using the symbol or or variables and expressing...

Discrete Mathematics With Applications

For each function of an angle, write the cofunction of the complement of the angle. sin49

Mathematics For Machine Technology

Evaluating a Line Integral Using Greens TheoremIn Exercises 1524, use Greens Theorem to evaluate the line integ...

Multivariable Calculus

A breeder of show dogs is interested in the number of female puppies in a litter. If a birth is equally likely ...

Introduction To Statistics And Data Analysis

The average price for a gallon of gasoline in the United States is 3.73 and in Russia itis 3.40 (Bloomberg Busi...

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

Reminder Round all answers to two decimal places unless otherwise indicated. Velocity GivenA particle is moving...

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

64. The Pew Research Center surveyed adults who own/use the following technologies:Â Internet, smartphone, email...

Essentials Of Statistics For Business & Economics

Identify the statistical procedure used to determine a correlation for different types of data and explain what...

Research Methods for the Behavioral Sciences (MindTap Course List)

Sketching a Quadric SurfaceIn Exercises 1526, classify and sketch the quadric surface. Use a computer algebra s...

Calculus (MindTap Course List)

Define a main effect for one factor and an interaction between factors, and be able to identify main effects an...

Research Methods for the Behavioral Sciences (MindTap Course List)

Refer to the Costello Music Company problem in exercise 49. a. Using time series decomposition, compute the sea...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

In Exercises 15-17, use the properties of logarithms to expand the expression as a sum, difference, and/or cons...

College Algebra

y=4x2+1 defines y implicitly as a function of x.

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

The acceleration for a particle whose position at time t is is:

Study Guide for Stewart's Multivariable Calculus, 8th

In Exercises 73-76, match the equation of the hyperbole with its graph. x225y29=1 a. b. c. d.

College Algebra (MindTap Course List)