Timeline for answer to What's the difference between the automorphism and isomorphism of graph? by Fredrik Meyer
Current License: CC BY-SA 3.0
Post Revisions
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 10, 2024 at 2:25 | comment | added | An5Drama | If someone struggled to understand the above, wikipedia defines automorphism as one permutation and isomorphism as bijection. IMHO the difference is their codomains as the answer says. Examples for automorphism mathworld.wolfram.com/GraphAutomorphism.html and isomorphism en.wikipedia.org/wiki/Graph_isomorphism. | |
| May 29, 2015 at 7:00 | comment | added | user99914 | (Here's a follow up question asked my a new user, which should be put into the comment) @Fredrik Meyer What other differences exist except for different labels of edges and vertices between two graphs? Could you give an example? | |
| May 6, 2015 at 8:13 | comment | added | Fredrik Meyer | @user2820579 I guess that's one way of looking at it - though I wouldn' think too much of labellings. | |
| May 5, 2015 at 19:03 | comment | added | user2820579 | So suppose that I have $UG$, the only difference between a structure-preserving isomorphism and automorphism is that for example, in an isomorphism I label a pair of isomorphic graphs from $1,\dots,6$ and the other with $a,\dots,f$; while in an automorphism I have to label both sets from $1,\dots,6$. Is this picture right? | |
| May 11, 2014 at 14:38 | vote | accept | Eden Harder | ||
| May 11, 2014 at 14:30 | comment | added | Fredrik Meyer | @EdenHarder Okay, I see your problem. The answer is still the same - an automorphism is just an isomorphism from $G$ to $G$. However, it could be that your source are using different definitions. | |
| May 11, 2014 at 12:55 | comment | added | Eden Harder | Thanks! I update the question. | |
| May 11, 2014 at 12:48 | comment | added | Fredrik Meyer | @EdenHarder They key word in the page you're linking to is the word "structure preserving". That means exactly that all the vertex-edge incidences are preserved. | |
| May 11, 2014 at 12:34 | comment | added | Eden Harder | Thanks! I update the question. | |
| May 11, 2014 at 11:26 | comment | added | Fredrik Meyer | @EdenHarder I don't understand what you mean. An isomorphism is structure-preserving as well, so it preservers the edge-vertex connectivity. | |
| May 11, 2014 at 11:11 | comment | added | Eden Harder | Not all the isomorphism from the graph $G$ to $G$ itself is automorphism. Since automorphism preserving the edge–vertex connectivity. | |
| May 11, 2014 at 10:02 | history | answered | Fredrik Meyer | CC BY-SA 3.0 |