Timeline for Eigenvalue of Perturbed Cayley Graph

6 events

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Jan 18, 2017 at 13:52	history	bumped	CommunityBot		This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
Dec 19, 2016 at 13:17	history	bumped	CommunityBot		This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
Nov 19, 2016 at 13:16	answer	added	Ken W. Smith		timeline score: 1
Nov 19, 2016 at 1:33	comment	added	Pat Devlin		And as for your post, the eigenvalues ought to be real because they're eigenvalues of a symmetric matrix. (And they are in fact real.)
Nov 19, 2016 at 1:31	comment	added	Pat Devlin		Hi. The graph you start with before adding that extra edge is called a circulant graph. Its spectrum is well-known. For instance, say we view the vector space C^V as functions from V to C. Then for each fixed c in Z_p, we get a function $f_c (x) = e^{2 \pi i c x /p}$ (a character of the group $\mathbb{Z}_p$). These are eigenfunctions with eigenvalues $\omega ^{-2c} + \omega^{-c} + \omega^{c} + \omega^{2c},$ where $\omega = e^{2 \pi i /p}.$ Didn't think about the extra edge, but think about what happens to these characters to understand it.
Nov 18, 2016 at 19:45	history	asked	john mangual	CC BY-SA 3.0