Sequences of Graphs...

Brendan McKay bdm at
Thu Dec 5 15:45:46 CET 2002

* N. J. A. Sloane <njas at> [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.  


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