A059687 Number of basic circuits of nullity n.

1, 1, 1, 2, 4, 14, 57

Offset

1,4

Comments

Appears to be the same as number of 3-connected cubic graphs on 2, 4, 6, 8, 10, 12 and 14 vertices. - Gordon F. Royle, Jun 02 2003

References

R. M. Foster, Geometrical circuits of electrical networks, Transactions of the American Institute of Electrical Engineers, 51 (1932), 309-317.

R. M. Foster, Topologic and algebraic considerations in network synthesis, pp. 8-18 in Proceedings of the Symposium on Modern Network Synthesis, New York, 1952, pp. 8-18. Polytechnic Institute of Brooklyn, New York, N. Y., 1952.

A. Krapez, S. K. Simic, D. V. Tosic, Parastrophically uncancellable quasigroup equations, Aequat. Math. 79 (3) (2010) 261-280 doi:10.1007/s00010-010-0016-3

Links

Table of n, a(n) for n=1..7.

Example

n=2: 3 edges in parallel between 2 nodes; n=3: K_4; n=4: K_{3,3} and the trivalent graph with 6 nodes and 9 edges formed by the 1-skeleton of a triangular prism.

Crossrefs

Cf. A002631, A204198.

Sequence in context: A306150 A030962 A030830 * A030909 A030809 A030958

Adjacent sequences: A059684 A059685 A059686 * A059688 A059689 A059690

Keyword

nonn,nice

Author

N. J. A. Sloane, Feb 06 2001

Status

approved