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

%I M1517

%S 1,2,5,18,100,1242,43425,4925635,1678993887,1613875721946,

%T 4293014800909806,31574944534364259507,644483327087699659771857,

%U 36676558984788056550610362834,5846161177591490590945591554686844,2621219060849255874034814155021919844156

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

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

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

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

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

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

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

%D 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).

%D R. W. Robinson, personal communication.

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

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

%H F. C. Bussemaker, P. J. Cameron, J. J. Seidel, and S. V. Tsaranov, <a href="https://www.researchgate.net/publication/241872284_Tables_of_signed_graphs ">Tables of signed graphs</a>, Report-WSK 91-01, Eindhoven University of Technology, Department of Mathematics and Computing Science, Eindhoven, 1991, 105 pp. (MR: 92g:05001).

%H P. J. Cameron, <a href="https://doi.org/10.1007/BF01215145">Cohomological aspects of two-graphs</a>, Math. Zeit., 157 (1977), 101-119.

%Y Cf. A002854, A084565, A004102.

%K nonn,nice

%O 1,2

%A _N. J. A. Sloane_

%E Extended by _N. J. A. Sloane_ from Robinson's table, Oct 20 2006

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

%E Corrected by _Vladeta Jovovic_, Apr 04 2009

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Last modified May 6 13:04 EDT 2021. Contains 343585 sequences. (Running on oeis4.)