Timeline for 1 or -1 as an eigenvalue of graph
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2012 at 8:52 | answer | added | Dima Pasechnik | timeline score: 4 | |
| Nov 2, 2012 at 8:37 | comment | added | Dima Pasechnik | I recall there was a paper by Babai where he related eigenvalues of Cayley graphs with characters of underlying groups: Babai, László Spectra of Cayley graphs. J. Combin. Theory Ser. B 27 (1979), no. 2, 180–189. | |
| Oct 19, 2012 at 0:46 | comment | added | Gordon Royle | What is "too large"? There are some pretty good packages out there. | |
| Oct 19, 2012 at 0:37 | comment | added | Aaron Meyerowitz | Tell us more about the graph and group. Are there elements of low order? What is their action on the group like? | |
| Oct 18, 2012 at 20:10 | comment | added | Moh514 | Many thanks for your answers. Yes, it is cayley graph, and it is too large. | |
| Oct 18, 2012 at 17:55 | answer | added | Aaron Meyerowitz | timeline score: 1 | |
| Oct 18, 2012 at 11:42 | comment | added | Brendan McKay | To continue Chris's comment, if you compute the eigenvector of $\pm 1$ in some small examples, you might see a pattern that you can generalize. Note that an eigenvector permuted according to a group element is also an eigenvector, so probably there will be an eigenvector with not many different entry values. Perhaps one which is constant on the blocks of a block system of the group. | |
| Oct 18, 2012 at 11:17 | comment | added | Chris Godsil | The simplest way to show that some number is an eigenvalue is to produce the eigenvector. The second-simplest, if you have the adjacency matrix, is to stuff it into something like sage and compute the factored characteristic polynomial. If you graph is given as a Cayley graph (for example) and is too large for the above strategies, you may be out of luck because then your problem is NP-hard | |
| Oct 18, 2012 at 8:15 | answer | added | Delio Mugnolo | timeline score: 2 | |
| Oct 18, 2012 at 5:36 | history | asked | Moh514 | CC BY-SA 3.0 |