A007127 Definition (1): Number of unlabeled strength-2 Eulerian graphs with n nodes. (Formerly M1517)

1, 2, 5, 18, 100, 1242, 43425, 4925635, 1678993887, 1613875721946, 4293014800909806, 31574944534364259507, 644483327087699659771857, 36676558984788056550610362834, 5846161177591490590945591554686844, 2621219060849255874034814155021919844156

Offset

1,2

Comments

Definition (2): Number of Eulerian 2-multigraphs with n nodes.

Definition (3): Number of switching classes of signed graphs on n unlabeled nodes.

Definition (4): Number of switching classes of 2-multigraphs with n nodes.

From Vladeta Jovovic, Mar 15 2009: (Start)

Definition (1) is same as Definition (2).

Definition (3) is same as Definition (4). (End)

That Definition (2) is same as Definition (4) follows from Theorem 8.3 of Cameron (1977). - N. J. A. Sloane, Mar 22 2009

References

R. W. Robinson, personal communication.

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1980.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..16.

F. C. Bussemaker, P. J. Cameron, J. J. Seidel, and S. V. Tsaranov, Tables of signed graphs, Report-WSK 91-01, Eindhoven University of Technology, Department of Mathematics and Computing Science, Eindhoven, 1991, 105 pp. (MR: 92g:05001).

P. J. Cameron, Cohomological aspects of two-graphs, Math. Zeit., 157 (1977), 101-119.

Crossrefs

Cf. A002854, A084565, A004102.

Sequence in context: A333837 A075634 A322396 * A279207 A005639 A093730

Adjacent sequences: A007124 A007125 A007126 * A007128 A007129 A007130

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

Extended by N. J. A. Sloane from Robinson's table, Oct 20 2006

Edited by N. J. A. Sloane, Mar 30 2009. Does the Cameron paper provide a formula? What about the labeled version? (Compare A002854.)

Corrected by Vladeta Jovovic, Apr 04 2009

Status

approved