A049287 Number of nonisomorphic circulant graphs, i.e., undirected Cayley graphs for the cyclic group of order n.

1, 2, 2, 4, 3, 8, 4, 12, 8, 20, 8, 48, 14, 48, 44, 84, 36, 192, 60, 336, 200, 416, 188, 1312, 423, 1400, 928, 3104, 1182, 8768, 2192, 8364, 6768, 16460, 11144, 46784, 14602, 58288, 44424, 136128, 52488, 355200, 99880, 432576, 351424, 762608, 364724, 2122944, 798952, 3356408

Offset

1,2

Comments

Further values for (twice) squarefree and (twice) prime-squared orders can be found in the Liskovets reference.

Terms may be computed by filtering potentially isomorphic graphs of A285620 through nauty. - Andrew Howroyd, Apr 29 2017

Links

Andrew Howroyd, Table of n, a(n) for n = 1..70

V. Gatt, On the Enumeration of Circulant Graphs of Prime-Power Order: the case of p^3, arXiv:1703.06038 [math.CO], 2017.

V. A. Liskovets, Some identities for enumerators of circulant graphs, arXiv:math/0104131 [math.CO], 2001; J. Alg. Comb. 18 (2003) 189.

V. A. Liskovets and R. Poeschel, On the enumeration of circulant graphs of prime-power and squarefree orders.

Brendan McKay, Nauty home page.

R. Poeschel, Publications.

Eric Weisstein's World of Mathematics, Circulant Graph.

Eric Weisstein's World of Mathematics, Circulant Matrix.

Formula

There is an easy formula for prime orders. Formulae are also known for squarefree and prime-squared orders.

From Andrew Howroyd, Apr 24 2017: (Start)

a(n) <= A285620(n).

a(n) = A285620(n) for n squarefree or twice square free.

a(A000040(n)^2) = A038781(n).

a(n) = Sum_{d|n} A075545(d).

(End)

Mathematica

CountDistinct /@ Table[CanonicalGraph[CirculantGraph[n, #]] & /@ Subsets[Range[Floor[n/2]]], {n, 25}] (* Eric W. Weisstein, May 13 2017 *)

Crossrefs

Cf. A049297, A049288, A049289, A060966, A285620, A038781, A075545.

Sequence in context: A334878 A285330 A048676 * A285620 A185959 A006799

Adjacent sequences: A049284 A049285 A049286 * A049288 A049289 A049290

Keyword

nonn,nice

Author

Valery A. Liskovets

Extensions

a(48)-a(50) from Andrew Howroyd, Apr 29 2017

Status

approved