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Math Help - Question about a "closed walk" in a graph

  1. #1
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    SOLVED - Question about a "closed walk" in a graph

    Hi,

    I am wondering ...
    Given the following Graph:

    Question about a "closed walk" in a graph-150px-traversal_example.png
    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?
    Last edited by iwan1981; July 6th 2011 at 08:07 AM.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Question about a "closed walk" in a graph

    Quote Originally Posted by iwan1981 View Post
    Hi,

    I am wondering ...
    Given the following Graph:

    Click image for larger version. 

Name:	150px-Traversal_example.png 
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Size:	4.6 KB 
ID:	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.
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  3. #3
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    Re: Question about a "closed walk" in a graph

    Thanks for the answer ...

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

    Thanks,
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  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Question about a "closed walk" in a graph

    Quote Originally Posted by iwan1981 View Post
    Thanks for the answer ...

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

    Thanks,
    Yes,
    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

    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.
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  5. #5
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    Re: Question about a "closed walk" in a graph

    thanks for making this clear for me :-)
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