Timeline for Graphs and symmetries
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 14, 2023 at 18:25 | comment | added | superriemann | Thanks for your responses. I agree with this discussion. I wonder if the graph that is dual to Weyl chamber decomposition (replace every Weyl chamber by a vertex and draw an edge if there is a reflecting plane separating the chambers) will also have this property. I don't quite know what this graph is called. | |
| Nov 14, 2023 at 12:03 | comment | added | Jukka Kohonen | Also the graph cannot contain any odd cycles. | |
| Nov 14, 2023 at 9:48 | comment | added | Jukka Kohonen | Right, I think I was reading something wrong about the cut edges :) But yes, single edges, even cycles and cartesian products. | |
| Nov 14, 2023 at 8:53 | comment | added | Brendan McKay | For the reason Ilya stated, I don't think the class is closed under strong or tensor product. However, it seems to be closed under cartesian product. So we have the cartesian product of any number of single edges and even length cycles, not necessarily of the same length. I'm wondering if there can be any others. | |
| Nov 14, 2023 at 7:54 | comment | added | Ilya Bogdanov | Obviously, the graph is not only regular but vertex-transitive (if connected) | |
| Nov 14, 2023 at 7:53 | comment | added | Ilya Bogdanov | @JukkaKohonen I do not think complete graphs are such. The author says `'this isomorphism', perhaps meaning that the isomorphism is fixed, not that you consider the family of all isomorphisms between the parts... | |
| Nov 13, 2023 at 16:18 | comment | added | Jukka Kohonen | Some easy additions to your family are: even cycles, even-size complete graphs, Cartesian / tensor / strong products of members of the family (this includes the hypercubes). I don't know of a general characterization though. | |
| S Nov 13, 2023 at 13:30 | review | First questions | |||
| Nov 13, 2023 at 13:32 | |||||
| S Nov 13, 2023 at 13:30 | history | asked | superriemann | CC BY-SA 4.0 |