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

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

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

Definition (1) is same as Definition (2). - Vladeta Jovovic, Mar 15 2009

Definition (3) is same as Definition (4). - Vladeta Jovovic, Mar 15 2009

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

References

• 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).
• 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

• 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.

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