Timeline for Conjugate vertices and distinguishing properties
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Aug 29, 2015 at 21:30 | history | rollback | Ilmari Karonen |
Rollback to Revision 1
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| Jan 6, 2010 at 15:17 | comment | added | Hans-Peter Stricker | You say "just pick one representative for each conjugacy class": is this soft or hard (I do not know)? If we have the conjugacy classes we also have the distinguishing properties. Why do you say the both have "absolute nothing to do" with each other? | |
| Jan 6, 2010 at 14:16 | comment | added | Mariano Suárez-Álvarez | I do not know why you think it is hard to find the conjugate formulas... You just have to pick one representative for each conjugacy class and construct the corresponding formula. The complexity in finding the conjugacy class has absolutely nothing to do with 'distinguishing properties': it is just a hard problem. | |
| Jan 6, 2010 at 7:13 | comment | added | Hans-Peter Stricker | One remark: I have used the $\sim$ sign for conjugacy, in your formula I would have written $Rvw$. | |
| Jan 6, 2010 at 7:12 | comment | added | Hans-Peter Stricker | Thanks, Mariano, you are perfectly right, the first step is easy: to construct for each vertex a formula which holds for it and exactly those that are conjugate to it: Just take the full description and make free each single variable successively. The next steps are not so easy: to find the conjugate formulas (corresponding to conjugate vertices) and - last but not least - to find distinguishing formulas with a minimum number of variables. (I didn't mention this yet because I haven't seen that the question otherwise is trivial.) | |
| Jan 5, 2010 at 23:24 | history | edited | Mariano Suárez-Álvarez | CC BY-SA 2.5 |
Add an example
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| Jan 5, 2010 at 22:17 | comment | added | Mariano Suárez-Álvarez | Well, since you are using equality of vertices, you are indeed including equality in your language :) | |
| Jan 5, 2010 at 21:28 | comment | added | Hans-Peter Stricker | there is an x with Rvx and for each y holds: Rvy -> x = y | |
| Jan 5, 2010 at 21:24 | comment | added | Mariano Suárez-Álvarez | @Hans: how do you express the property "$v$ has exactly one neighbor" formally? | |
| Jan 5, 2010 at 21:21 | comment | added | Hans-Peter Stricker | I am not quite sure if I understand your answer: where do you think do I include equality (and which kind of)? And if it should be trivial to construct a "distinguishing family of properties w.r.t to G" - as you point out - I would have to revise my definition since I did not want to pose a trivial question (see my Question 3). | |
| Jan 5, 2010 at 20:21 | history | answered | Mariano Suárez-Álvarez | CC BY-SA 2.5 |