Explanation Theorem used: Euler theorem: “For a connected graph, the following statements are true, a) If all vertices are even, the graph has at least one Euler path, which is also an Euler circuit. b) If exactly two vertices are odd, the graph has at least one Euler path but no Euler circuits (each Euler path must begin at one of the odd vertices and it will end at the other odd vertex). c) If there are more than two odd vertices, the graph has neither an Euler path nor an Euler circuit”. Calculation: A complete graph contains edges between all possible pairs of vertices...

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Chapter 13.3, Problem 66E

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To explain: The fact that “If a complete graph has n vertices, every vertex has the same degree”; explain how to tell if a complete graph has an Euler path or circuit.

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Chapter 13.3, Problem 65E

Chapter 13.3, Problem 67E

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Chapter 13 Solutions

PRINT UPGRADE - ALEKS 360 MATH OUR WORLD

Ch. 13.1 - Prob. 1TTO Ch. 13.1 - The floor plan shown in Figure 14-7 is for a...Ch. 13.1 - Prob. 3TTO Ch. 13.1 - Draw a graph for my neighborhood, shown in Figure...Ch. 13.1 - Prob. 5TTO Ch. 13.1 - Prob. 6TTO Ch. 13.1 - Prob. 7TTO Ch. 13.1 - Prob. 8TTO Ch. 13.1 - Prob. 1E Ch. 13.1 - What is the difference between a loop and a...

Ch. 13.1 - What is the difference between a circuit and a...Ch. 13.1 - Draw two graphs that look physically different but...Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E Ch. 13.1 - Prob. 11E Ch. 13.1 - How does graph coloring apply to maps?Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Prob. 18E Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Prob. 20E Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Prob. 25E Ch. 13.1 - Prob. 26E Ch. 13.1 - Prob. 27E Ch. 13.1 - Prob. 28E Ch. 13.1 - Prob. 29E Ch. 13.1 - Prob. 30E Ch. 13.1 - For Exercises 3134, represent each figure using a...Ch. 13.1 - Prob. 32E Ch. 13.1 - Prob. 33E Ch. 13.1 - Prob. 34E Ch. 13.1 - Prob. 35E Ch. 13.1 - Prob. 36E Ch. 13.1 - For Exercises 3538, draw a graph to represent each...Ch. 13.1 - Prob. 38E Ch. 13.1 - Prob. 39E Ch. 13.1 - For Exercises 3942, draw a graph that represents...Ch. 13.1 - Prob. 41E Ch. 13.1 - Prob. 42E Ch. 13.1 - In Exercises 4350, use graph coloring to find the...Ch. 13.1 - Prob. 44E Ch. 13.1 - Prob. 45E Ch. 13.1 - Prob. 46E Ch. 13.1 - In Exercises 4350, use graph coloring to find the...Ch. 13.1 - Prob. 48E Ch. 13.1 - Prob. 49E Ch. 13.1 - Prob. 50E Ch. 13.1 - Prob. 51E Ch. 13.1 - Prob. 52E Ch. 13.1 - Prob. 53E Ch. 13.1 - Prob. 54E Ch. 13.1 - Prob. 55E Ch. 13.1 - Draw a graph that represents the street map in...Ch. 13.1 - Prob. 57E Ch. 13.1 - Prob. 58E Ch. 13.1 - Prob. 59E Ch. 13.1 - Prob. 61E Ch. 13.1 - Prob. 62E Ch. 13.1 - Prob. 63E Ch. 13.1 - (a)When a graph represents a map as in Exercise...Ch. 13.2 - Classify the paths shown in the graphs as Euler...Ch. 13.2 - Use Euler's theorem to determine if the graphs...Ch. 13.2 - Prob. 3TTO Ch. 13.2 - Prob. 4TTO Ch. 13.2 - Prob. 1E Ch. 13.2 - Prob. 2E Ch. 13.2 - Prob. 3E Ch. 13.2 - Prob. 4E Ch. 13.2 - Prob. 5E Ch. 13.2 - Prob. 6E Ch. 13.2 - Prob. 7E Ch. 13.2 - Prob. 8E Ch. 13.2 - For Exercises 710, decide whether each connected...Ch. 13.2 - Prob. 10E Ch. 13.2 - For Exercises 710, decide whether each connected...Ch. 13.2 - Prob. 12E Ch. 13.2 - For Exercises 1120, (a)State whether the graph has...Ch. 13.2 - Prob. 14E Ch. 13.2 - For Exercises 1120, (a)State whether the graph has...Ch. 13.2 - Prob. 16E Ch. 13.2 - For Exercises 1120, (a)State whether the graph has...Ch. 13.2 - Prob. 18E Ch. 13.2 - For Exercises 1120, (a)State whether the graph has...Ch. 13.2 - Prob. 20E Ch. 13.2 - For Exercises 1120, (a)State whether the graph has...Ch. 13.2 - For Exercises 1120, (a)State whether the graph has...Ch. 13.2 - Prob. 23E Ch. 13.2 - Prob. 24E Ch. 13.2 - Prob. 25E Ch. 13.2 - Prob. 26E Ch. 13.2 - Prob. 27E Ch. 13.2 - For Exercises 2126, draw a graph for the figures...Ch. 13.2 - Prob. 29E Ch. 13.2 - Prob. 30E Ch. 13.2 - Prob. 31E Ch. 13.2 - Prob. 32E Ch. 13.2 - Prob. 33E Ch. 13.2 - Prob. 34E Ch. 13.2 - For Exercises 33 and 34, determine if an Euler...Ch. 13.2 - For Exercises 33 and 34, determine if an Euler...Ch. 13.2 - Prob. 37E Ch. 13.2 - Prob. 39E Ch. 13.2 - Prob. 40E Ch. 13.2 - Draw some sample graphs and use them to discuss...Ch. 13.2 - Prob. 42E Ch. 13.2 - Prob. 43E Ch. 13.2 - Prob. 44E Ch. 13.2 - Prob. 45E Ch. 13.2 - Explain why the word connected is crucial...Ch. 13.2 - Prob. 47E Ch. 13.2 - Prob. 48E Ch. 13.3 - Prob. 1TTO Ch. 13.3 - Prob. 2TTO Ch. 13.3 - Prob. 3TTO Ch. 13.3 - The driving times in minutes between four cities...Ch. 13.3 - Prob. 5TTO Ch. 13.3 - Prob. 6TTO Ch. 13.3 - Prob. 7TTO Ch. 13.3 - What is the difference between a Hamilton path and...Ch. 13.3 - Prob. 2E Ch. 13.3 - Give an example of a problem in our world that can...Ch. 13.3 - Prob. 4E Ch. 13.3 - Prob. 5E Ch. 13.3 - Prob. 6E Ch. 13.3 - Describe what a typical traveling salesperson...Ch. 13.3 - Prob. 8E Ch. 13.3 - Prob. 9E Ch. 13.3 - Prob. 10E Ch. 13.3 - Prob. 11E Ch. 13.3 - Prob. 12E Ch. 13.3 - For Exercises 1118, find two different Hamilton...Ch. 13.3 - Prob. 14E Ch. 13.3 - Prob. 15E Ch. 13.3 - Prob. 16E Ch. 13.3 - For Exercises 1118, find two different Hamilton...Ch. 13.3 - Prob. 18E Ch. 13.3 - Prob. 19E Ch. 13.3 - Prob. 20E Ch. 13.3 - For Exercises 1118, find two different Hamilton...Ch. 13.3 - Prob. 22E Ch. 13.3 - Prob. 23E Ch. 13.3 - Prob. 24E Ch. 13.3 - For Exercises 1924, find two different Hamilton...Ch. 13.3 - Prob. 26E Ch. 13.3 - Prob. 27E Ch. 13.3 - Prob. 28E Ch. 13.3 - For Exercises 2528, find the number of Hamilton...Ch. 13.3 - Prob. 30E Ch. 13.3 - Prob. 31E Ch. 13.3 - For Exercises 29 and 30, use the brute force...Ch. 13.3 - For Exercises 3134, use the nearest neighbor...Ch. 13.3 - Prob. 34E Ch. 13.3 - Prob. 35E Ch. 13.3 - Prob. 36E Ch. 13.3 - Prob. 37E Ch. 13.3 - Prob. 38E Ch. 13.3 - Prob. 39E Ch. 13.3 - Prob. 40E Ch. 13.3 - Prob. 41E Ch. 13.3 - For Exercises 3942, use the information in the...Ch. 13.3 - Prob. 43E Ch. 13.3 - Prob. 44E Ch. 13.3 - Prob. 45E Ch. 13.3 - For Exercises 4346, use the information in the...Ch. 13.3 - For Exercises 4346, use the information in the...Ch. 13.3 - For Exercises 45–48, use the information in the...Ch. 13.3 - Prob. 49E Ch. 13.3 - A pizza delivery person has five prearranged...Ch. 13.3 - Prob. 51E Ch. 13.3 - Prob. 52E Ch. 13.3 - Prob. 53E Ch. 13.3 - Prob. 54E Ch. 13.3 - When planning routes, distance isnt always the key...Ch. 13.3 - Prob. 56E Ch. 13.3 - Repeat questions 51 through 54, choosing four...Ch. 13.3 - Prob. 58E Ch. 13.3 - Prob. 59E Ch. 13.3 - Prob. 60E Ch. 13.3 - Find a road atlas that has a mileage chart. Pick...Ch. 13.3 - Prob. 62E Ch. 13.3 - Prob. 63E Ch. 13.3 - Prob. 64E Ch. 13.3 - Prob. 65E Ch. 13.3 - Prob. 66E Ch. 13.3 - Prob. 67E Ch. 13.3 - Prob. 68E Ch. 13.3 - Prob. 69E Ch. 13.3 - Prob. 70E Ch. 13.3 - Prob. 71E Ch. 13.3 - Prob. 72E Ch. 13.3 - Prob. 73E Ch. 13.3 - Prob. 74E Ch. 13.4 - Prob. 1TTO Ch. 13.4 - Prob. 2TTO Ch. 13.4 - Prob. 3TTO Ch. 13.4 - Prob. 4TTO Ch. 13.4 - Prob. 5TTO Ch. 13.4 - Prob. 1E Ch. 13.4 - Prob. 2E Ch. 13.4 - Prob. 3E Ch. 13.4 - Prob. 4E Ch. 13.4 - Prob. 5E Ch. 13.4 - Prob. 6E Ch. 13.4 - For Exercise 716, decide whether or not each graph...Ch. 13.4 - Prob. 8E Ch. 13.4 - Prob. 9E Ch. 13.4 - Prob. 10E Ch. 13.4 - Prob. 11E Ch. 13.4 - Prob. 12E Ch. 13.4 - Prob. 13E Ch. 13.4 - Prob. 14E Ch. 13.4 - Prob. 15E Ch. 13.4 - Prob. 16E Ch. 13.4 - Prob. 17E Ch. 13.4 - Prob. 18E Ch. 13.4 - Prob. 19E Ch. 13.4 - Prob. 20E Ch. 13.4 - Prob. 21E Ch. 13.4 - Prob. 22E Ch. 13.4 - Prob. 23E Ch. 13.4 - Prob. 24E Ch. 13.4 - Prob. 25E Ch. 13.4 - Prob. 26E Ch. 13.4 - Prob. 27E Ch. 13.4 - Prob. 28E Ch. 13.4 - Prob. 29E Ch. 13.4 - Prob. 30E Ch. 13.4 - Prob. 31E Ch. 13.4 - Prob. 32E Ch. 13.4 - Prob. 33E Ch. 13.4 - As a new suburban neighborhood is being built, the...Ch. 13.4 - Prob. 35E Ch. 13.4 - Prob. 36E Ch. 13.4 - Prob. 37E Ch. 13.4 - Prob. 38E Ch. 13.4 - Prob. 39E Ch. 13.4 - In the last two sections, we used both Hamilton...Ch. 13.4 - Prob. 41E Ch. 13.4 - Prob. 42E Ch. 13.4 - Prob. 43E Ch. 13.4 - Prob. 44E Ch. 13 - Use the graph shown in Figure 14-62 for Exercise...Ch. 13 - Prob. 2RE Ch. 13 - Prob. 3RE Ch. 13 - Prob. 4RE Ch. 13 - Prob. 5RE Ch. 13 - Prob. 6RE Ch. 13 - Use the graph shown in Figure 14-62 for Exercises...Ch. 13 - Prob. 8RE Ch. 13 - Prob. 9RE Ch. 13 - Prob. 10RE Ch. 13 - Prob. 11RE Ch. 13 - Prob. 12RE Ch. 13 - Prob. 13RE Ch. 13 - Repeat Exercise 13 for the graphs from Exercises...Ch. 13 - Prob. 15RE Ch. 13 - Prob. 16RE Ch. 13 - Prob. 17RE Ch. 13 - Prob. 18RE Ch. 13 - Prob. 19RE Ch. 13 - Prob. 20RE Ch. 13 - Prob. 21RE Ch. 13 - Prob. 22RE Ch. 13 - Prob. 23RE Ch. 13 - Prob. 24RE Ch. 13 - Prob. 25RE Ch. 13 - Prob. 26RE Ch. 13 - Prob. 27RE Ch. 13 - Prob. 28RE Ch. 13 - Prob. 29RE Ch. 13 - Prob. 30RE Ch. 13 - Prob. 31RE Ch. 13 - Prob. 32RE Ch. 13 - Prob. 33RE Ch. 13 - Prob. 34RE Ch. 13 - For the following graph: (a)What is the degree of...Ch. 13 - Draw a graph with two bridges, and the...Ch. 13 - Prob. 3CT Ch. 13 - Prob. 4CT Ch. 13 - (a)For the graph shown in Figure 14-73, find an...Ch. 13 - Prob. 6CT Ch. 13 - For the housing plan shown in Figure 14-75, draw a...Ch. 13 - Prob. 8CT Ch. 13 - Use the brute force method to find the shortest...Ch. 13 - Use the nearest neighbor method and cheapest link...Ch. 13 - Prob. 11CT Ch. 13 - Decide whether the problem can be solved using...

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The fact that “If a complete graph has n vertices, every vertex has the same degree”; explain how to tell if a complete graph has an Euler path or circuit.

Solution Summary: The author explains the Euler theorem: if a complete graph has n vertices, every vertex has the same degree.

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To explain: The fact that “If a complete graph has n vertices, every vertex has the same degree”; explain how to tell if a complete graph has an Euler path or circuit.

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Chapter 13 Solutions