Nikos,

> It seems that when the vertices are labelled 0,..., n-1 then the
> translation is simply 0 <-> n, and the rest is fixed.  At least
> this is the case with all examples I've seen.  Can I assume that
> this will allways be the case?

This is what happens. At first, the graph calls its relabel command
with no arguments. See

sage: G.relabel??

to see exactly what goes on there.
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