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

1,6

Comments

Every diameter k>0 occurs 4*k times.

See A370461 for the directed case.

Links

Table of n, a(n) for n=1..113.

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.

Formula

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

Example

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

Crossrefs

Cf. A370461.

Sequence in context: A059939 A071842 A344517 * A085141 A082896 A079416

Adjacent sequences: A371352 A371353 A371354 * A371356 A371357 A371358

Keyword

nonn

Author

Miquel A. Fiol, Mar 19 2024

Status

approved