Finding Self Isomorphisms in Graphs

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Homework Help Overview

The discussion revolves around finding non-trivial self isomorphisms in graphs, specifically focusing on the concept of automorphisms. Participants are exploring the definitions and implications of self isomorphisms in the context of graph theory.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand the meaning of non-trivial self isomorphisms and questions whether it involves splitting the graph to find isomorphic parts. Another participant reflects on the definition of trivial isomorphisms and considers the implications of mapping vertices while preserving edge structure.

Discussion Status

Participants are actively seeking clarity on the concept of self isomorphisms, with some engaging in definitions and exploring the nature of automorphisms. There is acknowledgment of confusion, but also progress as one participant indicates they have resolved their misunderstanding with assistance.

Contextual Notes

There is mention of a TA providing help, indicating that external guidance is being sought to clarify the concepts discussed. The original poster expresses uncertainty about the terminology and the process involved in identifying self isomorphisms.

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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.
 
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scorpius1782 said:

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.
 
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automorphism- Word I was looking for I guess. I'll be reading up on this. Thank you.
 
Edit: All wrong, figured it out with help from TA.
 

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