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This question concerns walks on the graph depicted in this diagramt First consider: walks of length 4 from a to d. (a) The to

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Answer #1

We wish to find walks of length 4 from a to d.

Here we note that the length of a walk is simply the number of edges passed in that walk.

Thus aabcd is a walk from a to d of length 4.

abcdd is a walk from a to d of length 4.

adadd is a walk from a to d of length 4.

The following are the walks of length 4 from a to d.

walks of length 4 from a to d 3 2 4 1 3 4 3 4 2 4 3 2 3 4 3 2 2 2 4 2 4

b) There is no path of length 4 from a to d, as in a path repeat of vertex is not allowed.

So number of paths of length 4 from a to d is 0.

c) As there is no path so there is no simple path.

d)

1 2 4 2 4 3 3 3 4 4 1 2 3 4 4 2 closed walk from a to a of length 4

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