[seqfan] Re: A conjecture concerning connected rooted strength 1 Eulerian graphs with n nodes

[franktaw at netscape.net]

Um, the Euler transform is not linear.

Franklin T. Adams-Watters


-----Original Message-----
From: Richard Mathar <mathar at strw.leidenuniv.nl>

vj> From seqfan-bounces at list.seqfan.eu Thu Mar 12 16:24:22 2009
vj> ...
vj> There is  Eric Weisstein's recent seq. A158007:  number of simple 
connected
noneulerian graphs on n nodes.
vj> Clearly  A158007(n) = A001349(n) - A003049(n).
vj>
vj> Interestingly, it appears that Euler transform of  A158007(n) gives
A007126(n+1).
vj> ...

If "E" is the Euler transform we have

A001349 -> E-> A000088

A003049 -> E-> A002854

So to show that
A158007 -> E -> A007126

you can equivalently show that A000088+A002854=A007126.
My graph theoretical background is too weak to address that
question.

RJM