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Archive for April, 2009

I’ve decided not to port over the posts from AoPS. Among other things, I’d prefer to preserve the comments on older posts as they are.

So here’s something I’ve been thinking about. Given a simple connected graph G, define \rho(G) to be its largest positive eigenvalue; in other words, if w_n counts the number of walks (equivalently, closed walks) of length n on G, then

\displaystyle \rho(G) = \limsup_{n \to \infty} \sqrt[n]{w_n}.

(more…)

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