BuyFind*arrow_forward*

4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.3, Problem 8ES

Textbook Problem

16 views

Show that the graph is planar by finding a planar drawing.

To determine

**To Prove:**

The given graph is a planar by finding a planar drawing.

**Given information:**

The graph is

**Definition used:**

__Planar graph: __A planar graph is a graph that can be drawn so that no edges intersect each other (except at vertices).

**Proof:**

Consider the graph with naming the vertices,

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 For each polynomial in Problems 1-4, give the degree of the polynomial, give the coefficient (numerical) of the...

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. x2x+1...

Finite Mathematics

Simplify the algebraic expressions in Problems 15-34 by removing parentheses and combining similar terms. Objec...

Intermediate Algebra

Limits from a Graph (a) Use the graph of f to find the following limits. (i) limxf(x) (ii) limxf(x) (b) State t...

Precalculus: Mathematics for Calculus (Standalone Book)

How would you remove the discontinuity of f? In other words, how would you define f(2) in order to make f conti...

Single Variable Calculus

Are the following graphs of functions? Explain. a. b. c. d.

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

The plane x + y + 2z = 2 intersects the paraboloid z = x2 + y2 in an ellipse. Find the points on this ellipse t...

Multivariable Calculus

For the following set of scores, find the value of each expression: a. X b. (X)2 c. X2 d. (X +3)

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

For each random variable defined here, describe the set of possible values for the variable, and state whether ...

Probability and Statistics for Engineering and the Sciences

Estimating Slope In Exercises 1 4, estimate the slope of the line.

Calculus: An Applied Approach (MindTap Course List)

In west Texas, water is extremely important. The following data represent pH levels in groundwater for a random...

Understanding Basic Statistics

Describe the difference in appearance between a bar graph and a histogram and describe the circumstances in whi...

Statistics for The Behavioral Sciences (MindTap Course List)

SOC A random sample of 100 cable TV movies contained an average of 3.38 acts of physical violence per program w...

Essentials Of Statistics

Find the most general antiderivative of the function. (Check your answer by differentiation.) r() = sec tan ...

Single Variable Calculus: Early Transcendentals, Volume I

Convert the expressions in Exercises 6584 to power form. 1(x2+1)334(x2+1)3

Finite Mathematics and Applied Calculus (MindTap Course List)

(a) Find the approximations T10 and M10 for 12e1/xdx. (b) Estimate the errors in the approximations of part (a)...

Calculus: Early Transcendentals

112 Find the area of the surface. The part of the plane 6x+4y+2z=1 that lies inside the cylinder x2+y2=25

Calculus (MindTap Course List)

Proof In Exercises 71-76, use integration by parts to prove the formula. (For Exercises 71-74, assume that n is...

Calculus: Early Transcendental Functions

Perform the indicated operation and write each result in scientific notation: 8.41083106

Elementary Technical Mathematics

Point V is in the exterior of circle Q not shown such that VQ is equal in length to the diameter of circle Q. C...

Elementary Geometry For College Students, 7e

Find the dimensions of the isosceles triangle of largest area that can be inscribed in a circle of radius r.

Single Variable Calculus: Early Transcendentals

In Exercises, let the binary operation be defined on by the given rule. Determine in each case whether a grou...

Elements Of Modern Algebra

Solve the equation. Check your solutions when necessary 3x2=7x1

Trigonometry (MindTap Course List)

Use the chart “The Rise of E-Books in Education” for Exercises 47-49.
48. What were the sales of education e-bo...

Contemporary Mathematics for Business & Consumers

FINANCIAL ANALYSIS The management of Acrosonic is faced with the problem of deciding whether to expand the prod...

Finite Mathematics for the Managerial, Life, and Social Sciences

Determining Convergence or Divergence In Exercises 9-30, determine the convergence or divergence of the series....

Calculus: Early Transcendental Functions (MindTap Course List)

Finding a Limit of a Trigonometric Function In Exercises 27-36, find the limit of the trigonometric function. l...

Calculus of a Single Variable

In the figure for Exercises 7 to 16, O is the center of the circle. See Theorem 6.3.5. Given: AE=x2,EB=12,DE=x+...

Elementary Geometry for College Students

Find each percentage. Round the answers to 2 decimal places when necessary. 18. 1.8% of 1240

Mathematics For Machine Technology

Foot Locker uses sales per square foot as a measure of store productivity. Sales are currently running at an an...

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

Let fx=x2-1and gx=2x+1. Find each function and its domain. fg

College Algebra (MindTap Course List)

A certain chromosome defect occurs in only 1 in 200 adult Caucasian males. A random sample of n = 100 adult Cau...

Introduction To Statistics And Data Analysis

The data contained in the DATAfile named FoodIndustry show the company/chain name, the average sales per store ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Finding an Equation of a PlaneIn Exercises 5760, find an equation of the plane that contains all the points tha...

Multivariable Calculus

Find for x = 3t2 + 1, y = t6 + 6t5.
t4 + 5t3
4t3 + 15t2

Study Guide for Stewart's Multivariable Calculus, 8th

Define counterbalancing and explain how it is used to minimize or eliminate threats to internal validity from t...

Research Methods for the Behavioral Sciences (MindTap Course List)

The y-coordinate of the center of mass of the region bounded by , x = 1, x = 5, y = 0 is:
4

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

Describe the different ways that within-subjects designs are used to compare two or more treatment conditions, ...

Research Methods for the Behavioral Sciences (MindTap Course List)

Finding a Particular Solution In Exercises 59-62, find the particular solution of the first-order linear differ...

Calculus (MindTap Course List)

If a and b are integers not both zero and if q and r are nonnegative integers such that a=bq+r then gcd(a,b)= .

Discrete Mathematics With Applications

In Exercise35-42, find a spanning tree for the given graph. Note:Answers will vary. The graph in Exercise 6

Mathematics: A Practical Odyssey

In Problems 3138 solve the given system of equations by either Gaussian elimination or Gauss-Jordan elimination...

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

Reminder Round all answers to two decimal places unless otherwise indicated. Driving Under the Influence: The W...

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

Volume of a Box A take-out fast-food restaurant is constructing an open box by cutting squares from the corners...

College Algebra

Differences in Insurance Claims Based on Marital Status. A large automobile insurance company selected samples ...

Essentials Of Statistics For Business & Economics

An Air Force introductory course in electronics uses a personalized system of instruction whereby each student ...

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