A337179 Number of geodetic graphs with n unlabeled vertices.

1, 1, 2, 4, 10, 23, 66, 185, 586, 1880, 6360, 21975, 78230, 283087, 1043329, 3895505, 14726263, 56234210, 216719056, 841857211, 3293753840, 12969219563

Offset: 1

Author

John Cu and Murray Elder, Jan 28 2021

Keywords

• nonn
• more

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.

Examples

			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
		

Links

• John Cu, AMSI Vacation Research Scholar project, 2021
• 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

Crossrefs

Cf. A337178, A001349.

Programs

Sage

See A337178.

Extensions

a(12)-a(22) from Florian Stober and Armin Weiß added by Murray Elder, Nov 14 2023