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: Some of the graphs with a loop are shown below in Figure 1. From Figure 1, it is observed that, in Figure 1 (a) loop is at the vertex A and it have an Euler circuit, Figure 1 (b) have loop is at D and it have an Euler circuit...

Connect Math hosted by ALEKS Access Card 52 Weeks for Math in Our World

3rd Edition

ISBN: 9781259232848

Author: David Sobecki, Allan Bluman

Publisher: McGraw-Hill Education

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Chapter 14.2, Problem 40E

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To discuss: Whether or not a graph with a loop can have an Euler circuit and prove the conjecture by using Euler’s theorem.

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Chapter 14.2, Problem 39E

Chapter 14.2, Problem 41E

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Chapter 14 Solutions

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Whether or not a graph with a loop can have an Euler circuit and prove the conjecture by using Euler’s theorem.

Solution Summary: The author explains Euler's theorem: if all vertices are even, the graph has at least one euler path, and two odd vertex graphs don't have one.

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To discuss: Whether or not a graph with a loop can have an Euler circuit and prove the conjecture by using Euler’s theorem.

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Chapter 14 Solutions