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Math Help - Isomorphic

  1. #1
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    Isomorphic

    Which of the following graphs (see attached) is not isomorphic to the others, and why?


    All graphs have 5 nodes
    All graphs have 6 arcs
    All graphs have 2 nodes of degree 3 and 3 nodes of degree 2
    No graph has parallel arcs
    No graphs have a loop
    All graphs have a cycle
    No graph is complete


    What other characteristics can I look for to prove that one of these 5 graphs is not isomorphic?


    (Also sorry for the bad paintbrush skills)
    Attached Thumbnails Attached Thumbnails Isomorphic-untitled.jpg  
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by meditate View Post
    Which of the following graphs (see attached) is not isomorphic to the others, and why?


    All graphs have 5 nodes
    All graphs have 6 arcs
    All graphs have 2 nodes of degree 3 and 3 nodes of degree 2
    No graph has parallel arcs
    No graphs have a loop
    All graphs have a cycle
    No graph is complete


    What other characteristics can I look for to prove that one of these 5 graphs is not isomorphic?


    (Also sorry for the bad paintbrush skills)
    How about the degee of the shortest cycle (that is the number of nodes in the closed cycle with the fewest nodes).

    RonL
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