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 AC , none of them is a bridge, so choose any edges from AB and AC . Choose the edge AB , name it as 1. Now the position is at the vertex B , there three choices for edge: Edge BC , BD and BE , none of them is a bridge. Choose the edge BD and name it as 2. Now the position is at the vertex D , there three choices for edges DG , DH and DE , none of them is a bridge. Choose the edge DG and name it as 3. Now the position is at the vertex G , there is only one choice GH . Choose the edge GH and name it as 4. Now the position is at the vertex H , there three choices for edge: Edge HD , HE and HI , none of them is a bridge. Choose the edge HI and name it as 5. Now the corresponding graph is shown below in Figure 2. Now the current position is at the vertex I , there are three choices for edge are edge IE , IF and IJ , none of them is a bridge...

A Survey of Mathematics with Applications (10th Edition) - Standalone book

10th Edition

ISBN: 9780134112107

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

Publisher: PEARSON

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Chapter 13.2, Problem 43E

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An Euler circuit by using the Fleury’s algorithm.

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A Survey of Mathematics with Applications (10th Edition) - Standalone book

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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