|
Search: id:A054981
|
|
|
| A054981 |
|
Number of certain connected weighted pseudo-graphs. |
|
+0
1
|
| |
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
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 Univerity, 2000, tbp, (for n >= 1)
|
|
EXAMPLE
|
n=0: V1=2, e=1,f=1; n=1: V3=1, V1=3, e=3, c=0; V3=1,V1=1,e=2,c=1; n=3: ...
|
|
CROSSREFS
|
Sequence in context: A119752 A111001 A055258 this_sequence A059449 A065907 A031272
Adjacent sequences: A054978 A054979 A054980 this_sequence A054982 A054983 A054984
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
Edwin Vargas (edwin.vargas(AT)physik.uni-karlsruhe.de), May 30 2000
|
|
|
Search completed in 0.002 seconds
|
