1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.

  2. jcsd
  3. Mar 9, 2014 #2


    User Avatar
    Homework Helper

    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.

    Attached Files:

    Last edited: Mar 11, 2014
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted