[seqfan] Re: A conjecture concerning connected rooted strength 1 Eulerian graphs with n nodes
mathar at strw.leidenuniv.nl
Thu Mar 12 17:27:32 CET 2009
vj> From seqfan-bounces at list.seqfan.eu Thu Mar 12 16:24:22 2009
vj> From: "Vladeta Jovovic" <vladeta at eunet.yu>
vj> To: <seqfan at list.seqfan.eu>
vj> Subject: [seqfan] A conjecture concerning connected rooted strength 1 Eulerian graphs with n nodes
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> Interestingly, it appears that Euler transform of A158007(n) gives A007126(n+1).
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
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