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Math Help - are them isomorphic?

  1. #1
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    are them isomorphic?

    if yes then why? if no then why?
    I appreciate your help very much. Thank you
    Attached Thumbnails Attached Thumbnails are them isomorphic?-_34.jpg   are them isomorphic?-_36.jpg   are them isomorphic?-_38.jpg   are them isomorphic?-_40.jpg   are them isomorphic?-_42.jpg  

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  2. #2
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    I will help you with #42. You must do the others for yourself.
    First, list the degree sequence for each graph.
    If the sequences are different then the graphs cannot be isomorphic.
    However, if they are the same that is no guarantee they are.
    The graphs in #42 have the same degree sequence: <1,1,1,1,1,1,1,3,4,4>.
    However, the two graphs are not isomorphic.
    Because the two vertices of degree 4 in the top graph are adjacent, while the two degree 4 vertices in the lower graph are not adjacent.

    There are others ways. Adjacency matrices can be used. Sometimes a simple inspection is enough.

    If they are isomorphic, you must find a mapping from one to another that preserves edges.
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