%I A002854 M0846 N0321
%S A002854 1,1,2,3,7,16,54,243,2038,33120,1182004,87723296,12886193064,
%T A002854 3633057074584,1944000150734320,1967881448329407496,
%U A002854 3768516017219786199856,13670271807937483065795200
%N A002854 Number of Euler graphs with n nodes; number of 2-graphs with n nodes; 
               and number of switching classes of graphs with n nodes.
%C A002854 Also called Eulerian graphs of strength 1.
%C A002854 "Switching" at a node complements all the edges incident with that node. 
               The illustration (see link) shows the 3 switching classes on 4 nodes.
%D A002854 Buekenhout, ed., Handbook of Incidence Geometry, 1995, p. 881.
%D A002854 F. C. Bussemaker, R. A. Mathon and J. J. Seidel, Tables of two-graphs, 
               T.H.-Report 79-WSK-05, Technological University Eindhoven, Dept. 
               Mathematics, 1979; also pp. 71-112 of "Combinatorics and Graph Theory 
               (Calcutta, 1980)", Lect. Notes Math. 885, 1981.
%D A002854 P. J. Cameron, Cohomological aspects of two-graphs, Math. Zeit., 157 
               (1977), 101-119.
%D A002854 P. J. Cameron and C. R. Johnson, The number of equivalence patterns of 
               symmetric sign patterns, Discr. Math., 306 (2006), 3074-3077.
%D A002854 CRC Handbook of Combinatorial Designs, 1996, p. 687.
%D A002854 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 
               1973, p. 114, (4.7.1).
%D A002854 Liskovec, V. A., Enumeration of Euler graphs. (Russian) Vesc Akad. Navuk 
               BSSR Ser. Fz.-Mat. Navuk 1970 1970 no. 6, 38-46.
%D A002854 C. L. Mallows and N. J. A. Sloane, Two-graphs, switching classes and 
               Euler graphs are equal in number, SIAM J. Appl. Math., 28 (1975), 
               876-880.
%D A002854 R. W. Robinson, Enumeration of Euler graphs, pp. 147-153 of F. Harary, 
               editor, Proof Techniques in Graph Theory. Academic Press, NY, 1969.
%D A002854 R. W. Robinson, Numerical implementation of graph counting algorithms, 
               AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1979.
%D A002854 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002854 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002854 R. W. Robinson, <a href="b002854.txt">Table of n, a(n) for n = 1..26</
               a>
%H A002854 P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               Sequences realized by oligomorphic permutation groups</a>, J. Integ. 
               Seqs. Vol. 3 (2000), #00.1.5.
%H A002854 N. J. A. Sloane, <a href="a2854.gif">Switching classes of graphs with 
               4 nodes.</a>
%H A002854 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               EulerianGraph.html">Link to a section of The World of Mathematics.</
               a>
%F A002854 There is an explicit formula (see any of the references, especially Mallows 
               and Sloane).
%Y A002854 Cf. A003049, A085618, A085619, A085620, A007127.
%Y A002854 Sequence in context: A143884 A122031 A089125 this_sequence A036356 A034732 
               A000278
%Y A002854 Adjacent sequences: A002851 A002852 A002853 this_sequence A002855 A002856 
               A002857
%K A002854 nonn,easy,nice
%O A002854 1,3
%A A002854 N. J. A. Sloane (njas(AT)research.att.com).
%E A002854 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 18 2000