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. Consider islands as vertices and a common bridge between two islands as an edge between them. For example, if there is a bridge between island A and island B , then there is an edge connecting A and B . The graph that represents the given figure is shown below in Figure 1...

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

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ISBN: 9781259232848

Author: David Sobecki, Allan Bluman

Publisher: McGraw-Hill Education

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Chapter 14.2, Problem 21E

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Whether the graph has an Euler path, an Euler circuit or neither; find the Euler path or Euler circuit if it exists.

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Chapter 14.2, Problem 20E

Chapter 14.2, Problem 22E

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Use the graph to determine whether the path described is an Euler path, an Euler circuit, or neither. Explain your answer. D, C.E, B. A. С. В. F.E D. Choose the correct answer below. O A. The path described is an Euler path because every vertex is traveled exactly once. O B. The path described is neither an Euler path nor an Euler circuit because not every edge is traveled once. O C. The path described is an Euler circuit because it is an Euler path that begins and ends at the different vertices. O D. The path described is neither an Euler path nor an Euler circuit because at least one edge is traveled more than once. O E. The path described is an Euler path becanse every edge is traveled exactly once O F. The path described is an Euler circuit because it is an Euler path that begins and ends at the same vertex.

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e) Check whether the graph V has Hamilton circuit. If yes, exhibit one. B es e6 E es e1d e12 D Graph V

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

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Whether the graph has an Euler path, an Euler circuit or neither; find the Euler path or Euler circuit if it exists.

Solution Summary: The author explains the Euler theorem: if all vertices are even, the graph has at least one euler path, which is also an enumerable circuit.

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Whether the graph has an Euler path, an Euler circuit or neither; find the Euler path or Euler circuit if it exists.

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Chapter 14 Solutions