Open Problems in Representing State Spaces for Cultural Transmission Models

Seriation Graphs

How large is the space of Laplacian spectra on unlabelled trees with N vertices?

Cayley’s theorem tells us the number of possible unlabelled trees on \(N\) vertices: \(n^{n-2}\). This can be very large (e.g., for \(n=20\), around \(10^{23}\)). But the number of distinguishable Laplacian spectra may be much smaller. It is worth understanding how large this state space of spectra may be for different numbers of assemblages.

Is there a useful notion of the “spectrum” of a time varying graph?

References Cited