Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
3rd Edition
ISBN: 9780134689555
Author: Edgar Goodaire, Michael Parmenter
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 10.2, Problem 1E
To determine
The graph Hamiltonian orEulerian.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a
random sample of 1014 adults aged 18 and over. One of the questions was, "How many
cups of coffee, if any, do you drink on an average day?" The following table shows the
results obtained (Gallup website, August 6, 2012).
Number of Cups
per Day
0
1
2
3
4 or more
Number of
Responses
365
264
193
91
101
Define a random variable x = number of cups of coffee consumed on an average day. Let
x=4 represent four or more cups.
a. Develop a probability distribution for x.
b. Compute the expected value of x.
c. Compute the variance of x.
d. Suppose we are only interested in adults who drink at least one cup of coffee on an
average day. For this group, let y = the number of cups of coffee consumed on an
average day. Compute the expected value of y and compare it to the expected value of x.
Ten major college football bowl games were played in January 2010, with the University
of Alabama beating the University of Texas 37 to 21 to become the national champion
of college football. The results of the 10 bowl games follow (USA Today, January 8, 2010).
Bowl Game
Score
Outback
Gator
Auburn 38 Northwestern 35
Florida State 33 West Virginia 21
Capital One
Penn State 19 LSU 17
Rose
Ohio State 26 Oregon 17
Florida 51 Cincinnati 24
Sugar
Cotton
Alamo
Fiesta
Mississippi State 21 Oklahoma State 7
Texas Tech 41 Michigan State 31
Boise State 17 TCU 10
Orange
Iowa 24 Georgia Tech 14
Championship
Alabama 37 Texas 21
Predicted
Point Margin
Actual
Point Margin
5
3
1
12
3
-2
14
3
9
-4
-3
4
229740706
14
10
10
16
The predicted winning point margin was based on Las Vegas betting odds approximately
one week before the bowl games were played. For example, Auburn was predicted to beat
Northwestern in the Outback Bowl by five points. The actual winning point margin for Au-
burn was three points. A…
In 2007 the New York Times reported that the median annual household income in the United
States was $55,500 (New York Times website, August, 21, 2013). Answer the following
questions based on the following sample of 14 household incomes for 2013 ($1000s).
49.4
52.2
52.4
53.4
51.3
52.1
48.7
64.5
51.6
46.5
52.9
52.5
52.1
51.2
a.
What is the median household income for the sample data for 2013?
b. Based on the sample data, estimate the percentage change in the median household
income from 2007 to 2013.
c. Compute the first and third quartiles.
Chapter 10 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 10.1 - Prob. 1TFQCh. 10.1 - A path is a walk in which all vertices are...Ch. 10.1 - 3. A trail is a path
Ch. 10.1 - A path is trail.Ch. 10.1 - A cycle is a special type of circuit.Ch. 10.1 - 6. A cycle is a circuit with no repeated edges
Ch. 10.1 - 7. An Eulerian circuit is a cycle.
Ch. 10.1 - Prob. 8TFQCh. 10.1 - A sub graph of a connected graph must be...Ch. 10.1 - Prob. 10TFQ
Ch. 10.1 - K8,10 is Eulerian.Ch. 10.1 - Prob. 12TFQCh. 10.1 - 13. A graph with more than one component cannot be...Ch. 10.1 - Prob. 1ECh. 10.1 - [BB] Answer the Konigsberg bridge Problem and...Ch. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - 6. Suppose we modify the definition of Eulerian...Ch. 10.1 - 7. (a) Is there an Eulerian trail from A to B in...Ch. 10.1 - [BB] (Fictitious) A recently discovered map of the...Ch. 10.1 - 9. Euler’s original article about the Konigsberg...Ch. 10.1 - Prob. 10ECh. 10.1 - Prob. 11ECh. 10.1 - [BB] For which values of n1 , if any, is Kn...Ch. 10.1 - 13. (a) Find a necessary and sufficient condition...Ch. 10.1 - Prob. 14ECh. 10.1 - 15.[BB] Prove that any circuit in the graph must...Ch. 10.1 - Prob. 16ECh. 10.1 - Prob. 17ECh. 10.1 - Prob. 18ECh. 10.1 - Prob. 19ECh. 10.1 - Prob. 20ECh. 10.1 - Prob. 21ECh. 10.1 - Prob. 22ECh. 10.1 - Prob. 23ECh. 10.1 - Prob. 24ECh. 10.1 - 25. Prove that a graph is bipartite if and only if...Ch. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.2 - A Hamiltonian cycle is a circuit.
Ch. 10.2 - Prob. 2TFQCh. 10.2 - Prob. 3TFQCh. 10.2 - Prob. 4TFQCh. 10.2 - Prob. 5TFQCh. 10.2 - A graph that contains a proper cycle cannot be...Ch. 10.2 - Prob. 7TFQCh. 10.2 - Prob. 8TFQCh. 10.2 - Prob. 9TFQCh. 10.2 - Prob. 10TFQCh. 10.2 - Prob. 1ECh. 10.2 - 2. Determine whether or not each of the graphs of...Ch. 10.2 - Determine whether each of the graph shown is...Ch. 10.2 - Prob. 4ECh. 10.2 - Consider the graph shown. Is it Hamiltonian? Is...Ch. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Does the graph have a Hamiltonian cycle that...Ch. 10.2 - Prob. 9ECh. 10.2 - Prob. 10ECh. 10.2 - How many edges must a Hamiltonian cycle is kn...Ch. 10.2 - 12. Draw a picture of a cube, by imagining that...Ch. 10.2 - Prob. 13ECh. 10.2 - Prob. 14ECh. 10.2 - Prob. 15ECh. 10.2 - Prob. 16ECh. 10.2 - Suppose G is a graph with n3 vertices and at least...Ch. 10.2 - 18.[BB] Suppose G is a graph with vertices such...Ch. 10.2 - Prob. 19ECh. 10.2 - Prob. 20ECh. 10.2 - Answer true of false and in each case either given...Ch. 10.2 - Prob. 22ECh. 10.2 - Prob. 23ECh. 10.2 - Find a necessary and sufficient condition on m and...Ch. 10.3 - Prob. 1TFQCh. 10.3 - Prob. 2TFQCh. 10.3 - Prob. 3TFQCh. 10.3 - Prob. 4TFQCh. 10.3 - Prob. 5TFQCh. 10.3 - Prob. 6TFQCh. 10.3 - Prob. 7TFQCh. 10.3 - Prob. 8TFQCh. 10.3 - Prob. 9TFQCh. 10.3 - Prob. 10TFQCh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Prob. 7ECh. 10.3 - 8. (a) [BB] Find the adjacency matrices and of...Ch. 10.3 - 9. Repeat Exercise 8 for the graphs and shown....Ch. 10.3 - Prob. 10ECh. 10.3 - Let A=[abcpqrxyz] and let P=[010001100]. Thus P is...Ch. 10.3 - Prob. 12ECh. 10.3 - 13. For each pair of matrices shown, decide...Ch. 10.3 - 14. [BB] Let A be the adjacency matrix of a...Ch. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Prob. 17ECh. 10.3 - Prob. 18ECh. 10.4 - Prob. 1TFQCh. 10.4 - Prob. 2TFQCh. 10.4 - It is an open question as to whether there exists...Ch. 10.4 - Prob. 4TFQCh. 10.4 - Prob. 5TFQCh. 10.4 - Prob. 6TFQCh. 10.4 - Prob. 7TFQCh. 10.4 - Prob. 8TFQCh. 10.4 - Prob. 9TFQCh. 10.4 - Prob. 10TFQCh. 10.4 - Prob. 1ECh. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Prob. 9ECh. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.4 - 12. [BB] Could Dijkstra’s algorithm (original...Ch. 10.4 - Prob. 13ECh. 10.4 - 14. (a) If weights were assigned to the edges of...Ch. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10 - In the Konigsberg Bringe Problem (see fig. 9.1),...Ch. 10 - Prob. 2RECh. 10 - Suppose G1 and G2 are graphs with no vertices in...Ch. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Is the graph Hamiltonian? Is it Eulerian? Explain...Ch. 10 - Determine, with reason, whether each of the...Ch. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - 15. A connected graph G has 10 vertices and 41...Ch. 10 - Prob. 16RECh. 10 - Let v1,v2,........v8 and w1,w2,..........w12 be...Ch. 10 - Prob. 18RECh. 10 - Martha claims that a graph with adjacency...Ch. 10 - Prob. 20RECh. 10 - Which of the following three matrices (if any) is...Ch. 10 - Apply the first form of Dijkstras algorithm to the...Ch. 10 - Prob. 23RECh. 10 - 24. Apply the original form of Dijkstra’s...Ch. 10 - Apply the improved version of Dijkstras algorithm...Ch. 10 - Prob. 26RECh. 10 - 27. Apply the Floyd- Warshall algorithm apply to...Ch. 10 - Prob. 28RE
Knowledge Booster
Similar questions
- Evaluate the triple integral 3' 23 HIG 2 +3 f(x, y, z)dxdydz where f(x, y, z) = x + 2x-y ม u = v = and w = 2 2 3 Triple Integral Region R -2 x N 2 y 3arrow_forwardFind the volume of the solid bounded below by the circular cone z = 2.5√√√x² + y² and above by the sphere x² + y²+z² = 6.5z.arrow_forwardElectric charge is distributed over the triangular region D shown below so that the charge density at (x, y) is σ(x, y) = 4xy, measured in coulumbs per square meter (C/m²). Find the total charge on D. Round your answer to four decimal places. 1 U 5 4 3 2 1 1 2 5 7 coulumbsarrow_forward
- Let E be the region bounded cone z = √√/6 - (x² + y²) and the sphere z = x² + y² + z² . Provide an answer accurate to at least 4 significant digits. Find the volume of E. Triple Integral Spherical Coordinates Cutout of sphere is for visual purposes 0.8- 0.6 z 04 0.2- 0- -0.4 -0.2 04 0 0.2 0.2 x -0.2 04 -0.4 Note: The graph is an example. The scale and equation parameters may not be the same for your particular problem. Round your answer to 4 decimal places. Hint: Solve the cone equation for phi. * Oops - try again.arrow_forwardThe temperature at a point (x,y,z) of a solid E bounded by the coordinate planes and the plane 9.x+y+z = 1 is T(x, y, z) = (xy + 8z +20) degrees Celcius. Find the average temperature over the solid. (Answer to 4 decimal places). Average Value of a function using 3 variables z 1- y Hint: y = -a·x+1 * Oops - try again. xarrow_forwardFind the saddle pointsarrow_forward
- Problem #5 Section A of my math class has 110 students. Section B of my math class has 80 students. a). If I randomly select 15 students from the combined classes, in a way that the order of my selection does not matter, what is the probability that all 15 students can from Section A? b). If I randomly select 15 students from the combined classes, in a way that the order of my selection does not matter, what is the probability that all 15 students can from Section B? c). If I randomly select 15 students from the combined classes, in a way that the order of my selection does not matter, what is the probability that all 7 students come from section A and 8 students come from section B?arrow_forwardProblem #6 A special passcode to unlock your phone consists of 4 digits where repeated digits are not allowed. If someone were to randomly guess a 4 digit passcode, what is the probability that they guess your passcode on the first try?arrow_forwardProblem #3 If a card is picked at random from a standard 52-card deck, what is the probability of getting a black card or a queen?arrow_forward
- Problem #1 In the 2010 census, it was reported that the United States had a population of 310 million people. Of those, 74 million were under the age of 18. If you chose a person from the U.S. population at random, what is the probability they are under the age of 18? Problem #2 Given a set S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, if you were choosing a number at random what is the probability that you would choose an even number or a number larger than 7?arrow_forwardAnswer number twoarrow_forwardAnswer number onearrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL