Timeline for Spectral Graph Theory
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 13, 2014 at 0:01 | comment | added | Yemon Choi | @AlexDegtyarev presumably there are some constraints due to the Horn inequalities mathoverflow.net/questions/4224/eigenvalues-of-matrix-sums but that doesn't mean they are useful or better than "trivial constraints" | |
| Apr 14, 2014 at 8:43 | comment | added | Chris Godsil | None is known in general. | |
| Apr 14, 2014 at 4:33 | comment | added | user49525 | So there is no proper relation between these two spectra? @ChrisGodsil | |
| Apr 12, 2014 at 17:50 | comment | added | Chris Godsil | I offered only the "the short answer". For example, if the graph has one vertex of degree $k$ and the rest have degree $\ell$, you can derive an interlacing result. But I have never seen anyone find a useful connection between the two spectra. | |
| Apr 12, 2014 at 16:48 | comment | added | Alex Degtyarev | Hmm... I didn't ask. So, can you prove that there's no relation whatsoever? Meaning, that every pair of spectra can be realized by the two matrices of the same graph? | |
| Apr 12, 2014 at 16:28 | comment | added | Chris Godsil | Your comment is correct for the matrices, but you asked about the spectrum. | |
| Apr 12, 2014 at 15:28 | comment | added | Alex Degtyarev | I think this answer is not quite correct: there obviously is a relation, as the two matrices determine each other, just no one knows how to describe it :) | |
| Apr 12, 2014 at 13:59 | history | answered | Chris Godsil | CC BY-SA 3.0 |