DISCRETE MATHEMATICS WITH APPLICATION (
5th Edition
ISBN: 9780357097717
Author: EPP
Publisher: CENGAGE L
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 10.3, Problem 28ES
Prove that each of the properties in 21-29 is an invariant for graph isomorphism. Assume that n, m, and k are all nonnegative integers.
Has an Euler circuit
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
CClever Portal
CA
Co Managed bookmarks
ixl.com/math/geometry/surface-area-and-volume-review?ImsPlatform=1
IXL
My IXL
Learning
Assessment
Geometry > U.15 Surface area and volume review TER
C
Learn with an example or
► Watch a video
What is the surface area of this cone?
Use л ≈ 3.14 and round your answer to the nearest hundredth.
7 ft
8 ft
Submit
square feet
Type here to search
Work it out
Not feeling ready yet? These can help:
0
F1
1
2
F2
F3
#3
X
F4
C
F5
$
4
%
L
E
F6
+
回
F7
F8
F9
&
об г
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…
Chapter 10 Solutions
DISCRETE MATHEMATICS WITH APPLICATION (
Ch. 10.1 - Let G be a graph and let v and w be vertices in G....Ch. 10.1 - A graph is connected if, any only if, _____.Ch. 10.1 - Removing an edge from a circuit in a graph does...Ch. 10.1 - An Euler circuit in graph is _____.Ch. 10.1 - Prob. 5TYCh. 10.1 - Prob. 6TYCh. 10.1 - Prob. 7TYCh. 10.1 - If a graph G has a Hamiltonian circuit, then G has...Ch. 10.1 - A travelling salesman problem involves finding a...Ch. 10.1 - In the graph below, determine whether the...
Ch. 10.1 - In the graph below, determine whether the...Ch. 10.1 - Let G be the graph and consider the walk...Ch. 10.1 - Consider the following graph. How many paths are...Ch. 10.1 - Consider the following graph. How many paths are...Ch. 10.1 - An edge whose removal disconnects the graph of...Ch. 10.1 - Given any positive integer n, (a) find a connected...Ch. 10.1 - Find the number of connected components for each...Ch. 10.1 - Each of (a)—(c) describes a graph. In each case...Ch. 10.1 - Prob. 10ESCh. 10.1 - Is it possible for a citizen of Königsberg to make...Ch. 10.1 - Determine which of the graph in 12-17 have Euler...Ch. 10.1 - Determine which of the graph in 12-17 have Euler...Ch. 10.1 - Determine which of the graph in 12-17 have Euler...Ch. 10.1 - Determine which of the graph in 12-17 have Euler...Ch. 10.1 - Determine which of the graph in 12-17 have Euler...Ch. 10.1 - Determine which of the graph in 12-17 have Euler...Ch. 10.1 - Is it possible to take a walk around the city...Ch. 10.1 - For each of the graph in 19-21, determine whether...Ch. 10.1 - Prob. 20ESCh. 10.1 - Prob. 21ESCh. 10.1 - Prob. 22ESCh. 10.1 - Prob. 23ESCh. 10.1 - Find the complement of each of the following...Ch. 10.1 - Find the complement of the graph K4, the complete...Ch. 10.1 - Suppose that in a group of five people A,B,C,D,...Ch. 10.1 - Prob. 27ESCh. 10.1 - Show that at a party with at least two people,...Ch. 10.1 - Find Hamiltonian circuits for each of the graph in...Ch. 10.1 - Find Hamiltonian circuits for each of the graph in...Ch. 10.1 - Prob. 31ESCh. 10.1 - Show that none of graphs in 31-33 has a...Ch. 10.1 - Prob. 33ESCh. 10.1 - Prob. 34ESCh. 10.1 - Prob. 35ESCh. 10.1 - In 34-37, find Hamiltonian circuits for those...Ch. 10.1 - Prob. 37ESCh. 10.1 - Give two examples of graphs that have Euler...Ch. 10.1 - Prob. 39ESCh. 10.1 - Prob. 40ESCh. 10.1 - Give two examples of graphs that have Euler...Ch. 10.1 - A traveler in Europe wants to visit each of the...Ch. 10.1 - a. Prove that if a walk in a graph contains a...Ch. 10.1 - Prob. 44ESCh. 10.1 - Prob. 45ESCh. 10.1 - Prob. 46ESCh. 10.1 - Prove that if there is a trail in a graph G from a...Ch. 10.1 - If a graph contains a circuits that starts and...Ch. 10.1 - Prob. 49ESCh. 10.1 - Let G be a connected graph, and let C be any...Ch. 10.1 - Prob. 51ESCh. 10.1 - Prob. 52ESCh. 10.1 - For what values of n dies the complete graph Kn...Ch. 10.1 - For what values of m and n does the complete...Ch. 10.1 - What is the maximum number of edges a simple...Ch. 10.1 - Prob. 56ESCh. 10.1 - Prob. 57ESCh. 10.2 - In the adjacency matrix for a directed graph, the...Ch. 10.2 - Prob. 2TYCh. 10.2 - Prob. 3TYCh. 10.2 - Prob. 4TYCh. 10.2 - Prob. 5TYCh. 10.2 - Prob. 6TYCh. 10.2 - Find real numbers a, b, and c such that the...Ch. 10.2 - Find the adjacency matrices for the following...Ch. 10.2 - Find directed graphs that have the following...Ch. 10.2 - Find adjacency matrices for the following...Ch. 10.2 - Find graphs that have the following adjacency...Ch. 10.2 - Prob. 6ESCh. 10.2 - Prob. 7ESCh. 10.2 - Prob. 8ESCh. 10.2 - Prob. 9ESCh. 10.2 - Prob. 10ESCh. 10.2 - Prob. 11ESCh. 10.2 - Prob. 12ESCh. 10.2 - Let O denote the matrix [0000] . Find 2 × 2...Ch. 10.2 - Prob. 14ESCh. 10.2 - Prob. 15ESCh. 10.2 - In 14-18, assume the entries of all matrices are...Ch. 10.2 - Prob. 17ESCh. 10.2 - Prob. 18ESCh. 10.2 - Prob. 19ESCh. 10.2 - The following is an adjacency matrix for a graph:...Ch. 10.2 - Let A be the adjacency matrix for K3, the complete...Ch. 10.2 - Draw a graph that has [0001200011000211120021100]...Ch. 10.2 - Prob. 23ESCh. 10.3 - If G and G’ are graphs, then G is isomorphic to G’...Ch. 10.3 - A property P is an invariant for graph isomorphism...Ch. 10.3 - Prob. 3TYCh. 10.3 - For each pair of graphs G and G’ in 1-5, determine...Ch. 10.3 - For each pair of graphs G and G’ in 1-5, determine...Ch. 10.3 - For each pair of graphs G and G’ in 1-5, determine...Ch. 10.3 - For each pair of graphs G and G’ in 1-5, determine...Ch. 10.3 - For each pair of graphs G and G in 1—5, determine...Ch. 10.3 - For each pair of graphs G and G’ in 6-13,...Ch. 10.3 - For each pair of graphs G and G’ in 6-13,...Ch. 10.3 - For each pair of graphs G and G’ in 6-13,...Ch. 10.3 - Prob. 9ESCh. 10.3 - For each pair of graphs G and G’ in 6-13,...Ch. 10.3 - For each pair of graphs G and G’ in 6-13,...Ch. 10.3 - For each pair of simple graphs G and G in 6—13,...Ch. 10.3 - For each pair of graphs G and G’ in 6-13,...Ch. 10.3 - Draw all nonisomorphic simple graphs with three...Ch. 10.3 - Draw all nonisomorphic simple graphs with four...Ch. 10.3 - Prob. 16ESCh. 10.3 - Draw all nonisomorphic graphs with four vertices...Ch. 10.3 - Draw all nonisomorphic graphs with four vertices...Ch. 10.3 - Prob. 19ESCh. 10.3 - Draw four nonisomorphic graphs with six vertices,...Ch. 10.3 - Prob. 21ESCh. 10.3 - Prove that each of the properties in 21-29 is an...Ch. 10.3 - Prob. 23ESCh. 10.3 - Prove that each of the properties in 21-29 is an...Ch. 10.3 - Prob. 25ESCh. 10.3 - Prob. 26ESCh. 10.3 - Prob. 27ESCh. 10.3 - Prove that each of the properties in 21-29 is an...Ch. 10.3 - Prob. 29ESCh. 10.3 - Show that the following two graphs are not...Ch. 10.4 - A circuit-free graph is a graph with __________.Ch. 10.4 - Prob. 2TYCh. 10.4 - Prob. 3TYCh. 10.4 - Prob. 4TYCh. 10.4 - Prob. 5TYCh. 10.4 - Prob. 6TYCh. 10.4 - For any positive integer n, if G is a connected...Ch. 10.4 - Read the tree in Example 10.4.2 from left to right...Ch. 10.4 - Prob. 2ESCh. 10.4 - Prob. 3ESCh. 10.4 - Prob. 4ESCh. 10.4 - Prob. 5ESCh. 10.4 - Prob. 6ESCh. 10.4 - Prob. 7ESCh. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - Prob. 14ESCh. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - Prob. 17ESCh. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - In each of 8—21, either draw a graph with the...Ch. 10.4 - A connected graph has twelve vertices and eleven...Ch. 10.4 - A connected graph has nine vertices and twelve...Ch. 10.4 - Prob. 24ESCh. 10.4 - Prob. 25ESCh. 10.4 - If a graph has n vertices and n2 or fewer can it...Ch. 10.4 - A circuit-free graph has ten vertices and nine...Ch. 10.4 - Is a circuit-free graph with n vertices and at...Ch. 10.4 - Prob. 29ESCh. 10.4 - Prob. 30ESCh. 10.4 - a. Prove that the following is an invariant for...Ch. 10.5 - Prob. 1TYCh. 10.5 - Prob. 2TYCh. 10.5 - Prob. 3TYCh. 10.5 - Prob. 4TYCh. 10.5 - Prob. 5TYCh. 10.5 - Prob. 1ESCh. 10.5 - Prob. 2ESCh. 10.5 - Draw binary trees to represent the following...Ch. 10.5 - Prob. 4ESCh. 10.5 - Prob. 5ESCh. 10.5 - Prob. 6ESCh. 10.5 - Prob. 7ESCh. 10.5 - Prob. 8ESCh. 10.5 - Prob. 9ESCh. 10.5 - Prob. 10ESCh. 10.5 - Prob. 11ESCh. 10.5 - Prob. 12ESCh. 10.5 - Prob. 13ESCh. 10.5 - Prob. 14ESCh. 10.5 - Prob. 15ESCh. 10.5 - Prob. 16ESCh. 10.5 - Prob. 17ESCh. 10.5 - Prob. 18ESCh. 10.5 - Prob. 19ESCh. 10.5 - Prob. 20ESCh. 10.5 - Prob. 21ESCh. 10.5 - Prob. 22ESCh. 10.5 - Prob. 23ESCh. 10.5 - Prob. 24ESCh. 10.5 - In 21-25, use the steps of Algorithm 10.5.1 to...Ch. 10.6 - Prob. 1TYCh. 10.6 - Prob. 2TYCh. 10.6 - Prob. 3TYCh. 10.6 - In Kruskal’s algorithm, the edges of a connected,...Ch. 10.6 - Prob. 5TYCh. 10.6 - Prob. 6TYCh. 10.6 - At each stage of Dijkstra’s algorithm, the vertex...Ch. 10.6 - Prob. 1ESCh. 10.6 - Prob. 2ESCh. 10.6 - Prob. 3ESCh. 10.6 - Prob. 4ESCh. 10.6 - Prob. 5ESCh. 10.6 - Prob. 6ESCh. 10.6 - Prob. 7ESCh. 10.6 - Prob. 8ESCh. 10.6 - Prob. 9ESCh. 10.6 - Prob. 10ESCh. 10.6 - A pipeline is to be built that will link six...Ch. 10.6 - Use Dijkstra’s algorithm for the airline route...Ch. 10.6 - Use Dijkstra’s algorithm to find the shortest path...Ch. 10.6 - Use Dijkstra’s algorithm to find the shortest path...Ch. 10.6 - Use Dijkstra’s algorithm to find the shortest path...Ch. 10.6 - Use Dijkstra’s algorithm to find the shortest path...Ch. 10.6 - Prob. 17ESCh. 10.6 - Prob. 18ESCh. 10.6 - Prob. 19ESCh. 10.6 - Prob. 20ESCh. 10.6 - Prob. 21ESCh. 10.6 - Prob. 22ESCh. 10.6 - Prob. 23ESCh. 10.6 - Prob. 24ESCh. 10.6 - Prob. 25ESCh. 10.6 - Prob. 26ESCh. 10.6 - Prob. 27ESCh. 10.6 - Suppose a disconnected graph is input to Kruskal’s...Ch. 10.6 - Suppose a disconnected graph is input to Prim’s...Ch. 10.6 - Modify Algorithm 10.6.3 so that the output...Ch. 10.6 - Prob. 31ES
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- 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.arrow_forwardEvaluate 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_forward
- Electric 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_forwardLet 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_forward
- Find the saddle pointsarrow_forwardProblem #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_forward
- Problem #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_forwardProblem #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_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,
Elements Of Modern Algebra
Algebra
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Cengage Learning,
Graph Theory: Euler Paths and Euler Circuits; Author: Mathispower4u;https://www.youtube.com/watch?v=5M-m62qTR-s;License: Standard YouTube License, CC-BY
WALK,TRIAL,CIRCUIT,PATH,CYCLE IN GRAPH THEORY; Author: DIVVELA SRINIVASA RAO;https://www.youtube.com/watch?v=iYVltZtnAik;License: Standard YouTube License, CC-BY