1,3

Also called Eulerian graphs of strength 1.

"Switching" at a node complements all the edges incident with that node. The illustration (see link) shows the 3 switching classes on 4 nodes.

Buekenhout, ed., Handbook of Incidence Geometry, 1995, p. 881.

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.

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

P. J. Cameron and C. R. Johnson, The number of equivalence patterns of symmetric sign patterns, Discr. Math., 306 (2006), 3074-3077.

CRC Handbook of Combinatorial Designs, 1996, p. 687.

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 114, (4.7.1).

Liskovec, V. A., Enumeration of Euler graphs. (Russian) Vesc Akad. Navuk BSSR Ser. Fz.-Mat. Navuk 1970 1970 no. 6, 38-46.

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.

R. W. Robinson, Enumeration of Euler graphs, pp. 147-153 of F. Harary, editor, Proof Techniques in Graph Theory. Academic Press, NY, 1969.

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1979.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

R. W. Robinson, Table of n, a(n) for n = 1..26

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

N. J. A. Sloane, Switching classes of graphs with 4 nodes.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

There is an explicit formula (see any of the references, especially Mallows and Sloane).

Cf. A003049, A085618, A085619, A085620, A007127.

Sequence in context: A143884 A122031 A089125 this_sequence A036356 A034732 A000278

Adjacent sequences: A002851 A002852 A002853 this_sequence A002855 A002856 A002857

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 18 2000