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 states as vertices and common border as an edge between them. For example, if there is a common border between state MT and state ND , then there is an edge connecting MT and ND . The graph that represents the floor plan 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 31E

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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 30E

Chapter 14.2, Problem 32E

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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.

Draw a graph that models the connecting relationships in the floorplan below. The vertices represent the rooms and the edges represent doorways connecting rooms. Vertex F represents the outdoors. Determine whether the graph contains an Euler path or an Euler circuit. If either an Euler path or an Euler circuit exists, find one. PLEASE HELP

Chapter 14 Solutions

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

Ch. 14.1 - Draw a graph to represent ferry service between...Ch. 14.1 - The floor plan shown in Figure 14-7 is for a...Ch. 14.1 - Prob. 3TTO Ch. 14.1 - Draw a graph for my neighborhood, shown in Figure...Ch. 14.1 - Prob. 5TTO Ch. 14.1 - Prob. 6TTO Ch. 14.1 - Prob. 7TTO Ch. 14.1 - Prob. 8TTO Ch. 14.1 - Prob. 1E Ch. 14.1 - What is the difference between a loop and a...

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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