A359693 Number of edges in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n.

6, 24, 162, 670, 4456, 8942, 44470, 98902, 259114, 438552, 1330566, 1897164, 4893752, 7246502, 11544278, 17678880

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Jan 11 2023

Keywords

• nonn
• more

Comments

The number of vertices along each edge is A005728(n). No formula for a(n) is known.

See A359690 and A359692 for images of the graph.

Links

• Eric Weisstein's World of Mathematics, Complete Bipartite Graph.
• Wikipedia, Farey sequence.

Crossrefs

Cf. A359690 (vertices), A359691 (crossings), A359692 (regions), A359694 (k-gons), A005728, A290132, A359655, A358888, A358884, A006842, A006843.

Formula

a(n) = A359690(n) + A359692(n) - 2*A005728(n) + 1 by Euler's formula.