Mathematical Ideas with Integrated Review and Worksheets plus NEW MyLab Math with Pearson eText -- Access Card Package (Integrated Review Courses in MyLab Math and MyLab Statistics)
1st Edition
ISBN: 9780321977274
Author: Miller, Charles, Heeren, Vern, HORNSBY, John, Christopher
Publisher: PEARSON
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Chapter 14.3, Problem 29E
List all Hamilton circuits in the graph that start at P.
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Chapter 14 Solutions
Mathematical Ideas with Integrated Review and Worksheets plus NEW MyLab Math with Pearson eText -- Access Card Package (Integrated Review Courses in MyLab Math and MyLab Statistics)
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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- Complete a circuit starting at vertex s that passes through vertex uarrow_forwardFind a Hamilton circuit in the graph.arrow_forwardDraw a graph with two loops around vertex e, with end vertices a and f, with multiple edges on vertices b and c, and isolated vertex d. The order of the graph must be 8.arrow_forward
- Analyze each graph and explain why the graph does or does not have an Euler circuit. If it does, specify the nodes within the circuit.arrow_forwardDraw all graphs on 5 nodes in which every node has degree at most 2.arrow_forwardHow many edges are in the graph with n nodes where every pair of nodes are joined by an edge? Prove your answer.arrow_forward
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- Use the shortest path algorithm to find a shortest st-path in the following graph. The number on each edge indicates its length.arrow_forwardSuppose five players are competing in a tennis tournament. Each player needs to play every other player in a match (but not more than once). Each player will participate in no more than one match per day, and two matches can occur at the same time when possible. How many days will be required for the tournament? Represent the tournament as a graph, in which each vertex corresponds to a player and an edge joins two vertices if the corresponding players will compete against each other in a match. Next, color the edges, where each different color corresponds to a different day of the tournament. Because one player will not be in more than one match per day, no two edges of the same color can meet at the same vertex. If we can find an edge coloring of the graph that uses the fewest number of colors possible, it will correspond to the fewest number of days required for the tournament. Sketch a graph that represents the tournament, find an edge coloring using the fewest number of…arrow_forward2.) Determine how many backtracks are required to use every edge at least once returning to where you started. Indicate where the backtracks occur.arrow_forward
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