OFFSET
2,1
COMMENTS
Conjectured to be minimal number of nodes in any non-bipartite regular graph of degree n, diameter 2 and girth 4.
(5/2)*n <= a(n) <= 3*n-1, the lower limit corresponds to even n's, the upper limit to odd prime n's. - Zak Seidov, Apr 13 2012
REFERENCES
J. Sheehan, An extremal problem in finite graph theory, in: Infinite and finite sets (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. III, pp. 1235-1239. Colloq. Math. Soc. Janos Bolyai, Vol. 10, North-Holland, Amsterdam, 1975. MR0376429 (51 #12604).
LINKS
Amiram Eldar, Table of n, a(n) for n = 2..10000
FORMULA
a(n) = 3*n - A032742(n). - Amiram Eldar, May 27 2024
MATHEMATICA
a[n_] := (3 - 1/FactorInteger[n][[1, 1]]) * n; Array[a, 100, 2] (* Amiram Eldar, May 27 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 11 2012
STATUS
approved