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Self isomorphism

  1. Mar 9, 2014 #1
    1. The problem statement, all variables and given/known data
    I'm given a graph and am told to find non-trivial self isomorphisms. Non-trivial meaning that at least 1 node is "not mapped onto itself."

    I've tried looking for self isomorphism but I can't find anything. I can tell when two graphs are isomorphic through inspection but "self-isomorphism" doesn't make any sense to me. Does this mean I'm suppose to split the graph and find a two that are isomorphic? So cut a whole bunch of edges and see if I can make two isomorphic graphs??

    I'm just looking for clarity.

    Thanks.
     
  2. jcsd
  3. Mar 9, 2014 #2

    Zondrina

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    I believe a trivial isomorphism ##\phi## of a graph ##G## to another graph ##H## is an automorphism. For example, consider the identity map, which maps every node and edge onto itself (so really the graph wouldn't change at all, i.e ##G = H##).

    I think a non-trivial isomorphism would map the vertices in ##G## onto ##H##, preserving edge structure, but not necessarily the shape of the graph.
     
  4. Mar 9, 2014 #3
    automorphism- Word I was looking for I guess. I'll be reading up on this. Thank you.
     
  5. Mar 11, 2014 #4
    Edit: All wrong, figured it out with help from TA.
     

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    Last edited: Mar 11, 2014
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