# Question about a "closed walk" in a graph

• Jul 5th 2011, 10:12 AM
iwan1981
SOLVED - Question about a "closed walk" in a graph
Hi,

I am wondering ...
Given the following Graph:

Attachment 21781
A walk is just something like A, B, C, B, E

In a closed walk the "begin" vertex needs to be the same as the "end" vertex.
And we are allowed in that walk to use the vertices that we cross in out walk multiple times...
So a closed walk can be A, B, C, D, E, B, A.
Where "B" is used twice and the start/begin vertex is "A"

Now ... is it correct if I assume if this is a closed walk as well?
A, B, C, B, A

Or is this not allowed?
• Jul 5th 2011, 10:20 AM
Also sprach Zarathustra
Re: Question about a "closed walk" in a graph
Quote:

Originally Posted by iwan1981
Hi,

I am wondering ...
Given the following Graph:

Attachment 21781
A walk is just something like A, B, C, B, E

In a closed walk the "begin" vertex needs to be the same as the "end" vertex.
And we are allowed in that walk to use the vertices that we cross in out walk multiple times...
So a closed walk can be A, B, C, D, E, B, A.
Where "B" is used twice and the start/begin vertex is "A"

Now ... is it correct if I assume if this is a closed walk as well?
A, B, C, B, A

Or is this not allowed?

By your definition of "closed walk" A, B, C, B, A is allowed.
• Jul 5th 2011, 10:31 AM
iwan1981
Re: Question about a "closed walk" in a graph

So this means that A, B, A, B, A, B, C, B, A is also a closed walk?

Thanks,
• Jul 5th 2011, 10:49 AM
Also sprach Zarathustra
Re: Question about a "closed walk" in a graph
Quote:

Originally Posted by iwan1981

So this means that A, B, A, B, A, B, C, B, A is also a closed walk?

Thanks,

Yes,
Quote:

In a closed walk the "begin" vertex needs to be the same as the "end" vertex.
A, B, A, B, A, B, C, B, A

Quote:

we are allowed in that walk to use the vertices that we cross in out walk multiple times...
It happens in your walk A, B, A, B, A, B, C, B, A.

So, A, B, A, B, A, B, C, B, A closed walk.
• Jul 5th 2011, 11:07 AM
iwan1981
Re: Question about a "closed walk" in a graph
thanks for making this clear for me :-)