Timeline for Computing adjacency matrix eigenvalues by counting closed walks
Current License: CC BY-SA 4.0
6 events
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| Sep 7, 2020 at 23:57 | history | edited | Sam Hopkins | CC BY-SA 4.0 |
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| Sep 7, 2020 at 23:41 | comment | added | Richard Stanley | Exercises 1.6, 1.7, 1.8, and 1.10 of my book Algebraic Combinatorics, second ed., can be done by combinatorial reasoning, though there are also linear algebraic proofs. | |
| Sep 7, 2020 at 23:04 | comment | added | Asvin | Alternatively, you could make asymptotic statements: As the number of vertices goes to infinity, the number of closed walks of a random graph approaches something with probability one and so the eigenvalues also approach something with probability one... Of course, I think it isn't too hard to calculate the eigenvalues directly in either of these examples. | |
| Sep 7, 2020 at 23:01 | comment | added | Sam Hopkins | @Asvin: Perhaps you can make sense of closed walk counting for infinite graphs using some kind of normalization procedure, but naively even for $k=0$ we get $\infty$-many walks. | |
| Sep 7, 2020 at 22:07 | comment | added | Asvin | I would imagine that you can count the number of closed walks on a k-partite graph too, similar to a bipartite graph. Is there a version for infinite graphs - if so, the Rado graph seems doable too. | |
| Sep 7, 2020 at 17:33 | history | asked | Sam Hopkins | CC BY-SA 4.0 |