A054981 Number of certain connected weighted pseudo-graphs.

1, 2, 8, 14, 57, 161, 680

Offset

0,2

Comments

a(n) is the number of connected graphs, multi-edges and self-loops allowed, of weight n with vertices (nodes) of degree 1, 3 or 4 only. The weight of a 1-, 3-, 4-vertex is 0,1,2, respectively.

Number of edges: e = (V1+3*V3+4*V4)/2 = (3*n+V1-2*V4)/2; cyclomatic number c = 1-V+e = (n-V1+2)/2; where Vi is the number of i-vertices, i=1,3,4, V= V1+V3+V4 and n = V3+2*V4 is the weight.

References

E. Vargas, The SU(2)xU(1)xU(1) Extension of the Electroweak Standard Model, PhD thesis, Karlsruhe University, 2000, tbp, (for n >= 1).

Links

Table of n, a(n) for n=0..6.

Sean A. Irvine, Initial Terms of A054981

Sean A. Irvine, Java program (github)

Example

n=0: V1=2, e=1, f=1;
n=1: V3=1, V1=3, e=3, c=0;
n=2: V3=1, V1=1, e=2, c=1;
n=3: ...

Crossrefs

Sequence in context: A055258 A277649 A192777 * A059449 A272930 A140973

Adjacent sequences: A054978 A054979 A054980 * A054982 A054983 A054984

Keyword

nonn,more

Author

Edwin Vargas (edwin.vargas@gmx.de), May 30 2000

Extensions

a(5)-a(6) from Sean A. Irvine, Mar 07 2022

Status

approved