Thanks in advance!

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- April 6th 2008, 04:01 PMshawnMore Graph Questions
Thanks in advance!

- April 6th 2008, 05:21 PMPlato
You do know, I hope, that these definitions are not unique or standard.

So if we mean by a*walk*a sequence of alternating vertices and edges, beginning with a vertex and ending with a vertex, not necessarily the same.

A*path*is a walk in which all edges are distinct.

(Again these may not agree with your definitions)

So is a star-like graph with n+1 vertices, 0 to n, both “010” and “102” are walks but only “102” is a path.

Thus the number of walks of length two is . WHY?

But the number of paths of length two is . WHY? - April 6th 2008, 08:10 PMshawn
Your interpretation is correct.

The number of walks of length two is because you either just choose two edges from n (all the paths) or you can walk from 0 to any vertex and back and there are n ways to do this.

and the number of paths of length two is because you just choose two edges from n and because they are all adjacent through 0 you have your path. - April 7th 2008, 04:32 PMPlato
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If n=4 then

- April 7th 2008, 04:39 PMshawn