A049297 Number of nonisomorphic circulant digraphs (i.e., Cayley digraphs for the cyclic group) of order n.

1, 2, 3, 6, 6, 20, 14, 46, 51, 140, 108, 624, 352, 1400, 2172, 4262, 4116, 22040, 14602, 68016, 88376, 209936, 190746, 1062592, 839094, 2797000, 3728891, 11276704, 9587580, 67195520, 35792568

Offset

1,2

Comments

Terms may be computed by filtering potentially isomorphic graphs of A056391 through nauty. Terms computed in this way for a(25), a(27) agree with theoretical calculations by others. - Andrew Howroyd, Apr 23 2017

Links

Table of n, a(n) for n=1..31.

V. A. Liskovets, Some identities for enumerators of circulant graphs, arXiv:math/0104131 [math.CO], 2001.

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

R. Poeschel, Publications.

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

Victoria Gatt, Mikhail Klin, Josef Lauri, Valery Liskovets, From Schur Rings to Constructive and Analytical Enumeration of Circulant Graphs with Prime-Cubed Number of Vertices, in Isomorphisms, Symmetry and Computations in Algebraic Graph Theory, (Pilsen, Czechia, WAGT 2016) Vol. 305, Springer, Cham, 37-65.

Brendan McKay, Nauty home page.

Formula

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

From Andrew Howroyd, Apr 23 2017: (Start)

a(n) <= A056391(n).

a(n) = A056391(n) for squarefree n.

a(A000040(n)^2) = A038777(n).

(End)

Prog

(GAP)
LoadPackage("grape");
CirculantDigraphCount:= function(n) local g; # slow for n >= 10
g:=Graph( Group(()), [1..n], OnPoints, function(x, y) return (y-x) mod n = 1; end, false);
return Length(GraphIsomorphismClassRepresentatives(List(Combinations([1..n]), s->DistanceGraph(g, s))));
end; # Andrew Howroyd, Apr 23 2017

Crossrefs

Cf. A049287-A049289, A056391, A038777.

Sequence in context: A117777 A371991 A223547 * A285664 A056391 A056430

Adjacent sequences: A049294 A049295 A049296 * A049298 A049299 A049300

Keyword

nonn,nice

Author

Valery A. Liskovets

Extensions

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

a(14) corrected by Andrew Howroyd, Apr 23 2017

a(16)-a(31) from Andrew Howroyd, Apr 23 2017

Status

approved