Sequences of Graphs...
Gordon Royle
gordon at csse.uwa.edu.au
Thu Dec 5 07:58:41 CET 2002
I seek opinons on the following question:
Some sequences of graphs on n vertices are listed in the OEIS as starting
from "n=0" and some from "n=1" and some (such as A054581) simply get it
wrong - they claim to start from n=0, but actually start from n=1.
There is also some inconsistency.. for example, labelled trees start from
n=1, but unlabelled trees start from n=0.
In general, I am not sure that anything is gained by starting *any* graph
sequence from n=0 - it is often ambiguous or arbitrary to determine
whether or not the null graph has a certain property, because
otherwise equivalent definitions often break down when n=0.
Should "graph" entries be constrained to always start at n=1 or greater?
Should existing sequences be "retro-fitted" by eliminating all "zero"'th
terms (or should all be augmented by *adding* zero'th terms?). Or is
it caveat emptor?
--
Dr. Gordon F Royle, http://www.csse.uwa.edu.au/~gordon, gordon at csse.uwa.edu.au
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