A337178 Number of biconnected geodetic graphs with n unlabeled vertices.

0, 1, 1, 1, 2, 1, 3, 1, 3, 4, 3, 1, 9, 2, 4, 8, 6, 5, 13, 3, 13, 19, 11, 3, 32

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. A vertex v of a connected graph G is a cut vertex if G-v is disconnected. A connected graph G is biconnected if it has no cut vertices. To obtain this sequence, non-isomorphic (biconnected) graphs were generated using Brendan McKay's nauty program, then the geodetic property was checked on this output.

Examples

			For n=5 there are exactly a(5)=2 biconnected geodetic graphs: a 5-cycle and the complete graph on 5 vertices.
		

Links

• John Cu, Length of Embedded Circuits in Geodetic Graphs, 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, Pages 121-136.
• Florian Stober and Armin Weiß, Geodetic Graphs: Experiments and New Constructions, arXiv:2308.08970 [math.CO], 2023.
• Wikipedia, Geodetic graph

Crossrefs

Cf. A002218, A337179.

Extensions

a(12)-a(25) from Florian Stober and Armin Weiß added by Murray Elder, Nov 14 2023