[seqfan] Re: graphs with odd degrees

[Georgi Guninski]

On Wed, Apr 04, 2012 at 09:03:09AM -0700, Tanya Khovanova wrote:
> Hello all,
> 
> Me and my student are working on a project where we encountered graphs with all odd degrees. I couldn't find the sequence in the OEIS. Will someone like to generate it? 
> 
> 
> We submitted two sequences:
> A210345 The number of degree sequences of simple graphs with n vertices with all even degrees.
> and 
> A210346 The number of degree sequences of simple graphs with 2n vertices with all odd degrees.
> 
> The sequences need more terms. And I do not know how to enumerate graphs themselves.
> 
> Tanya
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/

For enumerating non-isomorphic I use naytu [1] geng.
You can parse the graphs in whatever language, but since nauty is
optional package for sage I use it from sage.

Attached is a sample sage implementation which agrees with your terms to
a(9).


[1] http://cs.anu.edu.au/~bdm/nauty/

-------------- next part --------------
def tanya2():
	"""
	A210345 The number of degree sequences of simple graphs with n vertices with all even degrees.
	"""
	an=[]
	MAXN=9
	for n in xrange(1,MAXN+1):
		gn=graphs.nauty_geng("%s"%n)
		cac={}
		for G in gn:
			d=G.degree_sequence()
			d.sort()
			d=tuple(d)
			v=uniq([i%2 for i in d])
			
			if v==[0]:
				cac[d]=1
		a=len(cac.keys())		
		print 'a(%s)=%s'%(n,a)
		an += [a]
	return an

an=tanya2()
an