I'm looking for the spectral gap of common graphs (alternatively, the mixing time of a (lazy) random walk on these graphs). Asymptotic values are fine. Assume that every node has a sufficient number of self-loops. (For regular graphs at least d many) Spectral gaps should be for example,
- Clique $O(1)$
- Star $O(1)$
- Expanders $O(1)$
- Binary tree $\Theta(1/n)$
- Cycle $\Theta(1/n^2)$
- Grid $\Theta(1/n)$
What about other classes? For example d-nary trees or graphs arising from preferential attachment (I believe these should have $O(1)$). I'm especially interested in graphs where the gap between conductance and spectral gap is very high (Does this happen when the degree is small?).
Cheers