A361135 The number of unlabeled connected fairly 4-regular multigraphs of order n, loops allowed.

1, 3, 8, 30, 118, 548, 2790, 16029, 101353, 706572, 5375249, 44402094, 395734706, 3786401086, 38711834576, 421217184135, 4860174299186, 59278045511959, 762055884150141, 10299293881159294, 145994591873294780, 2165938721141964179, 33564939201581495090, 542344644703485899950, 9122110321170144880053

Offset

1,2

Comments

Edges are undirected, vertices not labeled. "Fairly" means that each vertex has degree 4, but two of these edges do not connect to a second vertex; they are "fins" in CAD speak or "half-edges" in perturbation theory. The two fins may be attached to the same or to two different nodes. In the usual mathematical nomenclature these are connected graphs of order n+2 with two vertices of degree 1 and n vertices of degree 4, loops allowed.

Links

Table of n, a(n) for n=1..25.

H. Kleinert, A. Pelster, B. Kastening, and M. Bachmann, Recursive graphical construction of Feynman diagrams and their multiplicities in Phi^4 and Phi^2*A theory, Phys. Rev. E 62 (2) (2000), 1537 Table II.

R. J. Mathar, Illustrations

Crossrefs

Cf. A085549 (4-regular), A352174 (assuming rooted external legs).

Sequence in context: A151440 A213860 A360991 * A348662 A162560 A293250

Adjacent sequences: A361132 A361133 A361134 * A361136 A361137 A361138

Keyword

nonn,hard

Author

R. J. Mathar, Mar 02 2023

Extensions

Terms a(7) and beyond from Andrew Howroyd, Mar 05 2023

Status

approved