Mathematical Ideas (13th Edition) - Standalone book
13th Edition
ISBN: 9780321977076
Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren
Publisher: PEARSON
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Chapter 14.1, Problem 64E
(a)
To determine
To Graph: Chromatic number of 3 vertices complete graph is shown below.
(b)
To determine
To Graph: Chromatic number of 4 vertices graph with colouring method. The graph is shown below.
(c)
To determine
To Graph: Chromatic number of given graph using colouring method. The graph is shown below.
(d)
To determine
General principle related to chromatic number of complete graph. Chromatic number of a graph is the minimum number of colours needed to produce a proper colouring of a graph.
(e)
To determine
Supporting reason about statement (d).
(f)
To determine
General condition for chromatic number of graph with complete sub-graph.
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Consider the following.
Do
(a) Give the number of edges in the graph.
(b) Give the number of vertices in the graph.
(c) Determine the number of vertices that are of odd degree.
(d) Determine whether the graph is connected.
O Yes
O No
(e) Determine whether the graph is a complete graph.
O Yes
O No
What is the smallest number of colors you need to properly color the vertices of K4,5? That is, find the chromatic number of the graph.
(a)
What is the degree of vertex
E
?
(b)
List all the even vertices and all the odd vertices.Click on "None" as needed.
List of the even vertices:
List of the odd vertices:
(c)
List all vertices that are adjacent to vertex
D
.Click on "None" as needed.
Chapter 14 Solutions
Mathematical Ideas (13th Edition) - Standalone book
Ch. 14.1 - Vertices and Edges In Exercises 1-6, determine how...Ch. 14.1 - Vertices and Edges In Exercises 1-6, determine how...Ch. 14.1 - Vertices and Edges In Exercises 1-6, determine how...Ch. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - Prob. 10E
Ch. 14.1 - Prob. 11ECh. 14.1 - Prob. 12ECh. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.1 - Prob. 16ECh. 14.1 - Prob. 17ECh. 14.1 - Prob. 18ECh. 14.1 - Prob. 19ECh. 14.1 - Prob. 20ECh. 14.1 - Prob. 21ECh. 14.1 - Prob. 22ECh. 14.1 - Prob. 23ECh. 14.1 - Prob. 24ECh. 14.1 - Prob. 25ECh. 14.1 - Number of Edges In Exercises 23-26, use the...Ch. 14.1 - Prob. 27ECh. 14.1 - Prob. 28ECh. 14.1 - Prob. 29ECh. 14.1 - Prob. 30ECh. 14.1 - Prob. 31ECh. 14.1 - Prob. 32ECh. 14.1 - Prob. 33ECh. 14.1 - Prob. 34ECh. 14.1 - Prob. 35ECh. 14.1 - Prob. 36ECh. 14.1 - Prob. 37ECh. 14.1 - Prob. 38ECh. 14.1 - Prob. 39ECh. 14.1 - Prob. 40ECh. 14.1 - Prob. 41ECh. 14.1 - Prob. 42ECh. 14.1 - Prob. 43ECh. 14.1 - 44. Chess Competition Students from two schools...Ch. 14.1 - Prob. 45ECh. 14.1 - Prob. 46ECh. 14.1 - Prob. 47ECh. 14.1 - Number of Handshakes There are seven people at a...Ch. 14.1 - Prob. 49ECh. 14.1 - Prob. 50ECh. 14.1 - Prob. 51ECh. 14.1 - 52. Students in the Same Class Mary, Erin, Sue,...Ch. 14.1 - Here is another theorem about graphs: In any...Ch. 14.1 - Draw two nonisomorphic (simple) graphs with 6...Ch. 14.1 - Explain why the two graphs drawn in Exercise 54...Ch. 14.1 - Analyzing a Cube with a Graph Draw a graph whose...Ch. 14.1 - Prob. 57ECh. 14.1 - Prob. 58ECh. 14.1 - Prob. 59ECh. 14.1 - Prob. 60ECh. 14.1 - Prob. 61ECh. 14.1 - Prob. 62ECh. 14.1 - Prob. 63ECh. 14.1 - Prob. 64ECh. 14.1 - Prob. 65ECh. 14.1 - Prob. 66ECh. 14.1 - Prob. 67ECh. 14.1 - Prob. 68ECh. 14.1 - Prob. 69ECh. 14.1 - Prob. 70ECh. 14.1 - 71. Inviting Colleagues to a Gathering Several of...Ch. 14.1 - Prob. 72ECh. 14.1 - Prob. 73ECh. 14.1 - Prob. 74ECh. 14.1 - Prob. 75ECh. 14.1 - Graph Coloring In Exercises 75 and 76, draw a...Ch. 14.1 - Prob. 77ECh. 14.1 - Prob. 78ECh. 14.1 - Prob. 79ECh. 14.1 - Prob. 80ECh. 14.1 - Prob. 81ECh. 14.1 - Prob. 82ECh. 14.1 - The Six Degrees of Kevin Bacon Use the Web site...Ch. 14.1 - The Six Degrees of Kevin BaconUse the Web site...Ch. 14.1 - The Six Degrees of Kevin BaconUse the Web site...Ch. 14.1 - The Six Degrees of Kevin Bacon Use the Web...Ch. 14.1 - The Six Degrees of Kevin Bacon Use the Web...Ch. 14.1 - The Six Degrees of Kevin Bacon Use the Web site...Ch. 14.1 - The Six Degrees of Kevin BaconUse the Web site...Ch. 14.1 - The Six Degrees of Kevin BaconUse the Web site...Ch. 14.1 - The Six Degrees of Kevin BaconUse the Web site...Ch. 14.1 - The Six Degrees of Kevin BaconUse the Web site...Ch. 14.1 - 93. Lines from She Walks in Beauty, by Lord...Ch. 14.1 - 94. Lines from Annabel Lee, by Edgar Allan Poe
It...Ch. 14.1 - Poetry Analysis Graphs may be used to clarify the...Ch. 14.1 - 96. Lines from Sailing to Byzantium, by William...Ch. 14.2 - Euler Circuits. In Exercises 1-3, a graph is shown...Ch. 14.2 - Prob. 2ECh. 14.2 - Euler Circuits In Exercises 1-3, a graph is shown...Ch. 14.2 - Prob. 4ECh. 14.2 - Euler's Theorem In Exercises 4-8, use Eulers...Ch. 14.2 - Prob. 6ECh. 14.2 - Euler's Theorem.In Exercises 4-8, use Eider's...Ch. 14.2 - Prob. 8ECh. 14.2 - Euler's Theorem In Exercises 9 and 10, use Eider's...Ch. 14.2 - Prob. 10ECh. 14.2 - Euler's Theorem In Exercises 11-14, use Eider's...Ch. 14.2 - Prob. 12ECh. 14.2 - Euler's Theorem In Exercises 11-14, use Euler's...Ch. 14.2 - Prob. 14ECh. 14.2 - Floor Tilings In Exercises 15-18, different floor...Ch. 14.2 - Prob. 16ECh. 14.2 - Floor Tilings In Exercises 15-18, different floor...Ch. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.2 - Prob. 20ECh. 14.2 - Prob. 21ECh. 14.2 - Prob. 22ECh. 14.2 - Fleury's Algorithm In Exercises 23-25, a graph is...Ch. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - Prob. 26ECh. 14.2 - Fleury's Algorithm In Exercises 26-28\ use...Ch. 14.2 - Prob. 28ECh. 14.2 - Euler's Theorem and Fleury's Algorithm In...Ch. 14.2 - Euler's Theorem and Fleury's Algorithm In...Ch. 14.2 - Euler's Theorem and Fleury's Algorithm In...Ch. 14.2 - Prob. 32ECh. 14.2 - 33. Parking Pattern The map shows the roads on...Ch. 14.2 - Prob. 34ECh. 14.2 - Floor Plans In Exercises 34-36, the floor plan of...Ch. 14.2 - Prob. 36ECh. 14.2 - Exercises 37-44 are based on the following...Ch. 14.2 - Prob. 38ECh. 14.2 - Exercises 37-44 are based on the following...Ch. 14.2 - Prob. 40ECh. 14.2 - Exercises 37-44 are based on the following...Ch. 14.2 - Floor PlansIn Exercises 41-43, refer to the floor...Ch. 14.2 - Prob. 43ECh. 14.2 - Prob. 44ECh. 14.2 - Prob. 45ECh. 14.2 - Prob. 46ECh. 14.2 - Prob. 47ECh. 14.2 - Prob. 48ECh. 14.2 - Prob. 49ECh. 14.2 - Route Planning For each street grid in Exercise...Ch. 14.2 - Route Planning For each street grid in Exercise...Ch. 14.2 - Route Planning For each street grid in Exercise...Ch. 14.3 - Prob. 1ECh. 14.3 - Prob. 2ECh. 14.3 - Euler and Hamilton Circuits In Exercises 3 and 4,...Ch. 14.3 - Euler and Hamilton Circuits In Exercises 3 and 4,...Ch. 14.3 - Hamilton Circuits In Exercises 5-10, determine...Ch. 14.3 - Hamilton Circuits In Exercises 5-10, determine...Ch. 14.3 - Hamilton Circuits In Exercises 5-10, determine...Ch. 14.3 - Hamilton Circuits In Exercises 5-10, determine...Ch. 14.3 - Hamilton Circuits In Exercises 5-10, determine...Ch. 14.3 - Hamilton Circuits In Exercises 5-10, determine...Ch. 14.3 - Prob. 11ECh. 14.3 - Prob. 12ECh. 14.3 - Prob. 13ECh. 14.3 - Decide whether each statement is true or false. If...Ch. 14.3 - Hamilton and Euler Circuits In Exercises 15-20,...Ch. 14.3 - Hamilton and Euler Circuits In Exercises 15-20,...Ch. 14.3 - Hamilton and Euler Circuits In Exercises 15-20,...Ch. 14.3 - Hamilton and Euler Circuits In Exercises 15-20,...Ch. 14.3 - Hamilton and Euler Circuits In Exercises 15-20,...Ch. 14.3 - Hamilton and Euler Circuits In Exercises 15-20,...Ch. 14.3 - FactorialsIn Exercises 21-24, use a calculator, if...Ch. 14.3 - Factorials In Exercises 21-24, use a calculator,...Ch. 14.3 - Factorials In Exercises 21-24, use a calculator,...Ch. 14.3 - Prob. 24ECh. 14.3 - Hamilton Circuit In Exercises 25-28, determine how...Ch. 14.3 - Prob. 26ECh. 14.3 - Prob. 27ECh. 14.3 - Prob. 28ECh. 14.3 - List all Hamilton circuits in the graph that start...Ch. 14.3 - Prob. 30ECh. 14.3 - Prob. 31ECh. 14.3 - Prob. 32ECh. 14.3 - Prob. 33ECh. 14.3 - Prob. 34ECh. 14.3 - Prob. 35ECh. 14.3 - Prob. 36ECh. 14.3 - Prob. 37ECh. 14.3 - Brute Force Algorithm In Exercises 38-41, use the...Ch. 14.3 - Brute Force Algorithm In Exercises 38-41, use the...Ch. 14.3 - Brute Force Algorithm In Exercises 38-41, use the...Ch. 14.3 - Brute Force Algorithm In Exercises 38-41, use the...Ch. 14.3 - Prob. 42ECh. 14.3 - Prob. 43ECh. 14.3 - Nearest Neighbor Algorithm In Exercises 42-44, use...Ch. 14.3 - 45. Nearest Neighbor Algorithm Refer to the...Ch. 14.3 - Prob. 46ECh. 14.3 - Prob. 47ECh. 14.3 - Prob. 48ECh. 14.3 - Prob. 49ECh. 14.3 - Hamilton Circuits In Exercises 47-50, find all...Ch. 14.3 - Traveling Salesman Problem The diagram represents...Ch. 14.3 - Prob. 52ECh. 14.3 - The Icosian Game The graph below shows the Icosian...Ch. 14.3 - Prob. 54ECh. 14.3 - Dirac's Theorem Paul A. M. Dirac proved the...Ch. 14.4 - Prob. 1ECh. 14.4 - Prob. 2ECh. 14.4 - Prob. 3ECh. 14.4 - Prob. 4ECh. 14.4 - Prob. 5ECh. 14.4 - Prob. 6ECh. 14.4 - Prob. 7ECh. 14.4 - Prob. 8ECh. 14.4 - Prob. 9ECh. 14.4 - Prob. 10ECh. 14.4 - Prob. 11ECh. 14.4 - Tree or Not a Tree? In Exercises 11-13, determine...Ch. 14.4 - Prob. 13ECh. 14.4 - Prob. 14ECh. 14.4 - Trees and Cut Edges In Exercises 14-17, determine...Ch. 14.4 - Trees and Cut Edges In Exercises 14-17, determine...Ch. 14.4 - Prob. 17ECh. 14.4 - Prob. 18ECh. 14.4 - Prob. 19ECh. 14.4 - Prob. 20ECh. 14.4 - Prob. 21ECh. 14.4 - Prob. 22ECh. 14.4 - Prob. 23ECh. 14.4 - Prob. 24ECh. 14.4 - Prob. 25ECh. 14.4 - Prob. 26ECh. 14.4 - Prob. 27ECh. 14.4 - Prob. 28ECh. 14.4 - Prob. 29ECh. 14.4 - Prob. 30ECh. 14.4 - Prob. 31ECh. 14.4 - Prob. 32ECh. 14.4 - Prob. 33ECh. 14.4 - Town Water Distribution A town council is planning...Ch. 14.4 - Prob. 35ECh. 14.4 - Prob. 36ECh. 14.4 - Prob. 37ECh. 14.4 - Prob. 38ECh. 14.4 - Prob. 39ECh. 14.4 - For Exercise 34
Trees, Edges, and Vertices Work...Ch. 14.4 - 41. Suppose we have a tree with 10 vertices.
(a)...Ch. 14.4 - Prob. 42ECh. 14.4 - Prob. 43ECh. 14.4 - 44. Design of a Garden Maria has 12 vegetable and...Ch. 14.4 - Prob. 45ECh. 14.4 - Prob. 46ECh. 14.4 - Prob. 47ECh. 14.4 - Prob. 48ECh. 14.4 - Prob. 49ECh. 14.4 - Prob. 50ECh. 14.4 - Prob. 51ECh. 14.4 - Prob. 52ECh. 14.4 - Prob. 53ECh. 14.4 - Prob. 54ECh. 14.4 - Prob. 55ECh. 14.4 - Vertex/Edge Relationship In this exercise, we...Ch. 14 - Basic Concepts In Exercises 1-5, refer to the...Ch. 14 - Basic Concepts In Exercises 1-5, refer to the...Ch. 14 - Prob. 3TCh. 14 - Prob. 4TCh. 14 - Prob. 5TCh. 14 - Prob. 6TCh. 14 - Prob. 7TCh. 14 - Prob. 8TCh. 14 - Planning for Dinner Julia is planning to invite...Ch. 14 - Prob. 10TCh. 14 - Prob. 11TCh. 14 - Prob. 12TCh. 14 - Prob. 13TCh. 14 - Scheduling Exams A teacher at a high school must...Ch. 14 - Prob. 15TCh. 14 - Prob. 16TCh. 14 - Prob. 17TCh. 14 - Prob. 18TCh. 14 - Prob. 19TCh. 14 - Prob. 20TCh. 14 - Prob. 21TCh. 14 - Prob. 22TCh. 14 - Prob. 23TCh. 14 - Prob. 24TCh. 14 - Prob. 25TCh. 14 - 26. Nonisomorphic Trees Draw three nonisomorphic...Ch. 14 - Prob. 27TCh. 14 - Prob. 28TCh. 14 - Prob. 29TCh. 14 - Prob. 30TCh. 14 - Prob. 31TCh. 14 - Prob. 32T
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- To draw 140 in standard position, place the vertex at the origin and draw the terminal side 140 ______ from the _________________ a. clockwise, positive x-axis b. counterclockwise, positive x-axis c. counterclockwise, positive y -axis d. clockwise, positive y-axisarrow_forward(a.) the number of edges in the graph (b.) give the number of vertices in the graph (c.) determine the number of vertices that are of odd degree (d.) determine whether the graph is connected.arrow_forwardWhen n = 3, there are nonisomorphic simple graphs.arrow_forward
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