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
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.
(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
KEYWORD
nonn,nice
AUTHOR
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