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A337179 Number of geodetic graphs with n unlabeled vertices.

%I A337179 #80 Nov 15 2023 01:35:55
%S A337179 1,1,2,4,10,23,66,185,586,1880,6360,21975,78230,283087,1043329,
%T A337179 3895505,14726263,56234210,216719056,841857211,3293753840,12969219563
%N A337179 Number of geodetic graphs with n unlabeled vertices.
%C A337179 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.
%H A337179 John Cu, <a href="https://vrs.amsi.org.au/student-profile/john-cu/">AMSI Vacation Research Scholar project, 2021</a>
%H A337179 Brendan McKay and Adolfo Piperno, <a href="http://users.cecs.anu.edu.au/~bdm/nauty/">nauty and Traces</a>. [nauty and Traces are programs for computing automorphism groups of graphs and digraphs.]
%H A337179 K. R. Parthasarathy and N. Srinivasan, <a href="https://doi.org/10.1016/0095-8956(82)90063-6">Some general constructions of geodetic blocks</a>, Journal of Combinatorial Theory, Series B (33) Issue 2, October 1982, pp. 121-136.
%H A337179 Florian Stober and Armin Weiß, <a href="https://arxiv.org/abs/2308.08970">Geodetic Graphs: Experiments and New Constructions</a>, arXiv:2308.08970 [math.CO], 2023.
%H A337179 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GeodeticGraph.html">Geodetic Graph</a>
%H A337179 Wikipedia, <a href="https://en.wikipedia.org/wiki/Geodetic_graph">Geodetic graph</a>
%e A337179 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.
%e A337179                              o
%e A337179       o               o     /|\
%e A337179      / \              |    o-|-o
%e A337179   o-o---o, o-o-o-o, o-o-o,  \|/
%e A337179                              o
%o A337179 (Sage) See A337178.
%Y A337179 Cf. A337178, A001349.
%K A337179 nonn,more
%O A337179 1,3
%A A337179 John Cu and _Murray Elder_, Jan 28 2021
%E A337179 a(12)-a(22) from Florian Stober and Armin Weiß added by _Murray Elder_, Nov 14 2023