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A337179 Number of geodetic graphs with n unlabeled vertices. 1
1, 1, 2, 4, 10, 23, 66, 185, 586, 1880, 6360, 21975, 78230, 283087, 1043329, 3895505, 14726263, 56234210, 216719056, 841857211, 3293753840, 12969219563 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
A graph is geodetic if each pair of vertices is joined by a unique shortest path. To obtain this sequence, non-isomorphic graphs were generated using Brendan McKay's nauty program, then the geodetic property is checked on this output.
LINKS
Brendan McKay and Adolfo Piperno, nauty and Traces. [nauty and Traces are programs for computing automorphism groups of graphs and digraphs.]
K. R. Parthasarathy and N. Srinivasan, Some general constructions of geodetic blocks, Journal of Combinatorial Theory, Series B (33) Issue 2, October 1982, pp. 121-136.
Florian Stober and Armin Weiß, Geodetic Graphs: Experiments and New Constructions, arXiv:2308.08970 [math.CO], 2023.
Eric Weisstein's World of Mathematics, Geodetic Graph
Wikipedia, Geodetic graph
EXAMPLE
For n=4 there are a(4)=4 geodetic graphs: a triangle with another edge attached to one vertex, an edge path of length 3, a tripod of 3 edges joined at a common vertex, and a complete graph on 4 vertices.
o
o o /|\
/ \ | o-|-o
o-o---o, o-o-o-o, o-o-o, \|/
o
PROG
(Sage) See A337178.
CROSSREFS
Sequence in context: A210592 A206432 A124480 * A130967 A148087 A156806
KEYWORD
nonn,more
AUTHOR
John Cu and Murray Elder, Jan 28 2021
EXTENSIONS
a(12)-a(22) from Florian Stober and Armin Weiß added by Murray Elder, Nov 14 2023
STATUS
approved

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Last modified July 12 16:16 EDT 2024. Contains 374251 sequences. (Running on oeis4.)