Timeline for Laplacian spectrum for product graphs
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 15, 2022 at 11:25 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Feb 4, 2016 at 16:55 | answer | added | Delio Mugnolo | timeline score: 0 | |
| Sep 25, 2011 at 5:11 | answer | added | Babak Alinejad | timeline score: 0 | |
| Aug 10, 2011 at 22:15 | comment | added | Noam D. Elkies | Sorry, I indeed meant the adjacency matrix. If the graphs have constant degree then this also yields the spectrum of the graph Laplacian, but in general it's a different question. | |
| Aug 10, 2011 at 21:31 | answer | added | Chris Godsil | timeline score: 6 | |
| Aug 10, 2011 at 21:30 | comment | added | Jernej | I believe this pdf refers to the spectrum of the adjacency matrix and not the Laplacian. Otherwise I do not see how the eigenvalues of the tensor products are $\lambda_i \cdot \mu_j$ since this would immediately imply the tensor product is never connected - a contradiction. | |
| Aug 10, 2011 at 21:04 | comment | added | Alain Valette | See sections 1.4.6, 1.4.7 and 1.4.8 of homepages.cwi.nl/~aeb/math/ipm1.pdf | |
| Aug 10, 2011 at 20:41 | comment | added | Jernej | Wouldn't that imply that the tensor product is always disconencted, since the multiplicty of the eigenvalue 0 in the Laplacian of $G$, counts the number of connected components in $G$? | |
| Aug 10, 2011 at 19:34 | comment | added | Noam D. Elkies | For the tensor product it's $\lambda_i \cdot \mu_j$ (special case of the spectrum of the tensor product of any two linear operators). | |
| Aug 10, 2011 at 18:40 | history | asked | Jernej | CC BY-SA 3.0 |