Question

A graph is given to the right. a. Explain why the graph has at least one Euler path. b. Use trial and error or​ Fleury's Algorithm to find one such path starting at Upper A​, with Upper D as the fourth and seventh​ vertex, and with Upper B as the fifth vertex. A C B D E A graph has 5 vertices labeled A through E and 7 edges. The edges are as follows: Upper A Upper C, Upper A Upper B, Upper A Upper D, Upper C Upper D, Upper C Upper E, Upper B Upper D, Upper D Upper E. a. Choose the correct explanation below. A. It has exactly two odd vertices. Your answer is correct.B. It has exactly two even vertices. C. It has more than two odd vertices. D. All graphs have at least one Euler path. b. Drag the letters representing the vertices given above to form the Euler path.

Answer 1

Answer:

  a.  It has exactly two odd vertices

  b.  A C E D B A D C

Step-by-step explanation:

(a) There will not be an Euler path if the number of odd vertices is not 0 or 2. Here, the graph has exactly two odd vertices: A and C.

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(b) We are required to produce a path of the form {A, _, _, D, B, _, D, _}.

Starting at A, there is only one way to get to node D as the 4th node on the path: via C and E. Node B must follow. From B, there is exactly one way to cover the remaining three edges that have not been traversed so far.

The Euler path meeting the requirements is ...

  A C E D B A D C

It is shown by the arrows on the edges in the graph of the attachment.