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A371355
Minimum diameter of a Cayley graph on the cyclic group Z_n with two generators.
1
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
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
KEYWORD
nonn
AUTHOR
Miquel A. Fiol, Mar 19 2024
STATUS
approved