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A006924 Number of connected trivalent graphs with 2n nodes and girth exactly 4.
(Formerly M1526)
18
0, 0, 0, 1, 2, 5, 20, 101, 743, 7350, 91763, 1344782, 22160335, 401278984, 7885687604, 166870266608, 3781101495300 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
REFERENCES
CRC Handbook of Combinatorial Designs, 1996, p. 647.
Gordon Royle, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
F. C. Bussemaker, S. Cobeljic, L. M. Cvetkovic and J. J. Seidel, Computer investigations of cubic graphs, T.H.-Report 76-WSK-01, Technological University Eindhoven, Dept. Mathematics, 1976.
FORMULA
a(n) = A014371(n) - A014372(n).
CROSSREFS
Connected k-regular simple graphs with girth exactly 4: this sequence (k=3), A184944 (k=4), A184954 (k=5), A184964 (k=6), A184974 (k=7).
Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); specified g: A006923 (g=3), this sequence (g=4), A006925 (g=5), A006926 (g=6), A006927 (g=7).
Connected 3-regular simple graphs with girth at least g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).
Sequence in context: A039909 A009551 A323274 * A212580 A261779 A227096
KEYWORD
nonn,hard,more
AUTHOR
EXTENSIONS
Definition corrected to include "connected", and "girth at least 4" minus "girth at least 5" formula provided by Jason Kimberley, Dec 12 2009
STATUS
approved

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Last modified February 21 04:30 EST 2024. Contains 370219 sequences. (Running on oeis4.)