# Self isomorphism

1. Mar 9, 2014

### scorpius1782

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. Mar 9, 2014

### Zondrina

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.

3. Mar 9, 2014

### scorpius1782

automorphism- Word I was looking for I guess. I'll be reading up on this. Thank you.

4. Mar 11, 2014

### scorpius1782

Edit: All wrong, figured it out with help from TA.

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Last edited: Mar 11, 2014