Explanation Algorithm Used: Fleury’s Algorithm: To determine an Euler path or an Euler circuit: “A. Use Euler’s theorem to determine whether an Euler path or an Euler circuit exists. If one exists proceed with steps 2-5. B. 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. C. 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”. D. 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). E. Continue until each edges of the entire graph has been traced once”. The given graph is shown below in Figure 1. From Figure 1, it is observed that the vertices D and E are odd vertices. That is, this graph has exactly two odd vertices. Then by the Euler theorem part (b), this graph has at least one Euler path but no Euler circuits. To find the Euler path by the Fleury’s Algorithm, starts with either at A or at G (since, they are the odd vertices) and ends with the other vertex. Start with the vertex D , at vertex D there are two choices for edges: edge DA , and DC , none of them is a bridge, so choose any edges from DA and DC . Choose the edge DA , name it as 1. Now the position is at the vertex A , there is only one choice AB and hence name it as 2. Then the position is at the vertex B , there is only one choice BE and hence name it as 3. Now, the position is at the vertex E , there are two choices for edges are edge EF and EI . Choose the edge EF and name it as 4. Now the position is at the vertex F , there is only one choice FJ . So, name the edge FJ and name it as 5. Now the position is at the vertex J , there is only one choice JO , and name it as 6 ...

A Survey of Mathematics with Applications Plus MyLab Math with Pearson eText -- 18 Week Access Card Package

10th Edition

ISBN: 9780136208341

Author: Angel, Allen, Abbott, Christine, RUNDE, Dennis

Publisher: PEARSON

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Chapter 13.2, Problem 38E

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A Survey of Mathematics with Applications Plus MyLab Math with Pearson eText -- 18 Week Access Card Package

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 path by using the Fleury’s algorithm.

Solution Summary: The author explains the Fleury's Algorithm, which determines whether an Euler path exists or not.

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