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A085549 Number of isomorphism classes of connected 4-regular multigraphs of order n, loops allowed. 8
1, 2, 4, 10, 28, 97, 359, 1635, 8296, 48432, 316520, 2305104, 18428254, 160384348, 1506613063, 15180782537 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also the number of different potential face pairing graphs for closed 3-manifold triangulations.

REFERENCES

B. A. Burton, Minimal triangulations and normal surfaces, Ph.D. thesis, University of Melbourne, 2003.

B. A. Burton, Minimal triangulations and face pairing graphs, preprint, 2003.

B. A. Burton, Enumeration of non-orientable 3-manifolds using face-pairing graphs and union-find, Discrete and Computational Geometry, 38 (2007), 527-571.

LINKS

Table of n, a(n) for n=1..16.

B. A. Burton, Regina (3-manifold topology software).

B. A. Burton, Face pairing graphs and 3-manifold enumeration, arXiv:0307382

H. Kleinert, A. Pelster, B. Kastening, M. Bachmann, Recursive graphical construction of Feyman diagrams and their multiplicities in Phi^4 and Phi^2*A theory, Phys. Rev. E 62 (2) (2000), 1537 eq (4.20) or arXiv:hep-th/9907168

B. Martelli and C. Petronio, Three-manifolds having complexity at most 9, Experiment. Math., Vol. 10 (2001), pp. 207-236

PROG

Can be generated using Regina (see link above), although generation is slow.

CROSSREFS

Cf. A129429, A129417, A005967, A129430, A129432, A129434, A129436, A118560.

Sequence in context: A090594 A188496 A191501 * A022492 A123429 A207018

Adjacent sequences:  A085546 A085547 A085548 * A085550 A085551 A085552

KEYWORD

hard,nonn

AUTHOR

Benjamin A. Burton (bab(AT)debian.org), Jul 04 2003

EXTENSIONS

a(12)-a(16) from Brendan McKay, Apr 15 2007, computed using software at http://users.cecs.anu.edu.au/~bdm/nauty/

Edited by N. J. A. Sloane, Oct 01 2007

STATUS

approved

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Last modified February 18 10:13 EST 2019. Contains 320250 sequences. (Running on oeis4.)