Explanation Algorithm Used: Fleury’s Algorithm: To determine an Euler path or an Euler circuit: “1. Use Euler’s theorem to determine whether an Euler path or an Euler circuit exists. If one exists proceed with steps 2-5. 2. If the graph has no odd vertices (therefore has at least one Euler circuit, which is also an Euler circuit), choose any vertex as the starting point. If the graph has exactly two odd vertices (therefore, has only an Euler path), choose one of the two odd vertices as the starting point. 3. Being to trace edges as you move through the graph. Number the edges as you trace them. Since you can’t trace any edges twice in Euler paths and Euler circuits, once an edge is traced consider it “invisible”. 4. When faced with a choice of edges to trace, if possible choose an edge that is not a bridge (that is, don’t create a disconnected graph with your choice of edges). 5. Continue until each edges of the entire graph has been traced once”. Calculation: The given graph is shown below in Figure 1. From Figure 1, it is observed that all the vertices even vertices. That is, the graph has no odd vertices. Then by the Euler theorem, this graph has at least one Euler path which is also an Euler circuit. To find the Euler circuit by the Fleury’s Algorithm starts with any vertex of the graph. Start with the vertex A , at vertex A there are two choices for edges: Edge AB and AD , none of them is a bridge, so choose any edges from AB and AD . Choose the edge AB , name it as 1. Now the position is at the vertex B , there is only one choice BE. Choose the edge BE and name it as 2. Now the position is at the vertex E , there three choices for edge are edge EF , ED , and EI , none of them is a bridge. Choose the edge EF and name it as 3. Now the position is at the vertex F , there is only one choice FJ . Choose the edge FJ and name it as 4. Now the position is at the vertex J , there is only one choice JI . Choose the edge JI and name it as 5...

A Survey of Mathematics with Applications plus MyLab Math Student Access Card -- Access Code Card Package (10th Edition)

10th Edition

ISBN: 9780134115764

Author: Allen R. Angel, Christine D. Abbott, Dennis Runde

Publisher: PEARSON

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Chapter 13.2, Problem 44E

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An Euler circuit by using the Fleury’s algorithm.

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Chapter 13.2, Problem 43E

Chapter 13.2, Problem 45E

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A Survey of Mathematics with Applications plus MyLab Math Student Access Card -- Access Code Card Package (10th Edition)

Ch. 13.1 - In Exercises 1-8, fill in the blanks with an...Ch. 13.1 - In Exercises 1-8, fill in the blanks with an...Ch. 13.1 - In Exercises 1-8, fill in the blanks with an...Ch. 13.1 - In Exercises 1-8, fill in the blanks with an...Ch. 13.1 - Prob. 5E Ch. 13.1 - In Exercises 1-8, fill in the blanks with an...Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - In Exercises 9-14, create a graph with the given...Ch. 13.1 - In Exercises 9-14, create a graph with the given...

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An Euler circuit by using the Fleury’s algorithm.

Solution Summary: The author explains the Fleury's Algorithm to determine an Euler circuit by using a graph with no odd vertices.

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An Euler circuit by using the Fleury’s algorithm.

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