Finding Self Isomorphisms in Graphs

[scorpius1782]

Homework Statement

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.

 

[STEMucator]

Homework Statement

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.

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.

 

[scorpius1782]

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

 

[scorpius1782]

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