Sequences of Graphs...
Brendan McKay
bdm at cs.anu.edu.au
Thu Dec 5 15:45:46 CET 2002
* N. J. A. Sloane <njas at research.att.com> [021206 01:22]:
> the main reason for beginning at n=0 is that you /can/ do so,
> and therefore the database entry /should/ do so. Because
> otherwise someone is going to look up the sequence with the zero term
> included and not find a match.
I can see this argument, but Gordon is correct that
1. the current state of the database is inconsistent; and
2. there are many cases where it is unclear whether the value
at n=0 is 0 or 1.
An excellent example of both was suggested by Gordon. Is the
null graph a tree? It is a connected graph with no cycles,
so it is a tree. It is not a connected graph with #edges
= #vertices - 1, so it is not a tree. If you want people to
be able to look it up starting at n=0, you need to add it
to the database twice, once with the null graph being a tree
and once with it not being a tree. And the same for very
many sequences which are types of trees and graphs.
Brendan.
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