A371355 Minimum diameter of a Cayley graph on the cyclic group Z_n with two generators.

0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset: 1

Author

Miquel A. Fiol, Mar 19 2024

Keywords

• nonn

Comments

Every diameter k>0 occurs 4*k times.

See A370461 for the directed case.

Examples

			For n=26..41 the Cayley graph Cay(n;4,5) (circulant) has diameter a(n)=4.
		

Links

• R. Beivide, E. Herrada, J. L. Balcazar, and A. Arruabarrena, Optimal distance networks of low degree for parallel computers, IEEE Trans. Comput. 40 (1991), no. 10, 1109-1124.

Crossrefs

Cf. A370461.

Formula

a(n) = ceiling((sqrt(2*n-1)-1)/2).