Sequences of Graphs...

Gordon Royle gordon at
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,, gordon at

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