OFFSET
1,2
COMMENTS
As usual, "graph" means "simple graph, without self-loops or multiple edges".
The graphs on 2n vertices all having odd degrees are just the complements of those having all even degrees. That's why the property of all odd degrees is seldom mentioned. Therefore this sequence is just every second term of A002854. - Brendan McKay, Apr 08 2012
LINKS
Sequence Fans Mailing List, Discussion, April 2012.
N. J. A. Sloane, The 16 graphs on 6 nodes
FORMULA
a(n) = A002854(2n).
EXAMPLE
The 3 graphs on 4 vertices are [(0, 3), (1, 3), (2, 3)], [(0, 2), (1, 3)], [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]: the tree with root of order 3, the disconnected graph consisting of two complete 2-vertex graphs, and the complete graph.
PROG
(Sage)
def graphsodddegree(MAXN=5):
"""
requires optional package "nauty"
"""
an=[]
for n in range(1, MAXN+1):
gn=graphs.nauty_geng("%s"%(2*n))
cac={}
a=0
for G in gn:
d = G.degree_sequence()
if all(i % 2 for i in d):
a += 1
print('a(%s)=%s'%(n, a))
an += [a]
return an
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Georgi Guninski, Apr 06 2012
EXTENSIONS
Terms from a(6) on added from A002854. - N. J. A. Sloane, Apr 08 2012
STATUS
approved