A038781 -id:A038781 - cp's OEIS frontend

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

Valery A. Liskovets

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

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.

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

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

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)

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

A038783 An intermediate sequence for nonisomorphic circulant undirected p^2-graphs, indexed by odd primes p.

Original entry on oeis.org

4, 10, 24, 208, 700, 8230, 29144, 381304, 19175140, 71582944, 3817763740, 54975633976, 209430787824, 3059510616424, 173215372864600, 9938978487990064, 38430716856090160, 2235968978631715024, 33731189163354610720, 131176846748288854980, 7749524484709164817824

Offset: 1

N. J. A. Sloane, May 04 2000

M. Klin, V. A. Liskovets and R. Poeschel, Analytical enumeration of circulant graphs with prime-squared vertices, Sem. Lotharingien de Combin., B36d, 1996, 36 pages.

Cf. A038781.

a(n) = A038782(n) - A038781(n) + A038784(n).

More terms from Valery A. Liskovets, May 09 2001

More terms and offset corrected by Sean A. Irvine, Feb 14 2021

A038784 An intermediate sequence for nonisomorphic circulant undirected p^2-graphs, indexed by odd primes p.

Original entry on oeis.org

4, 9, 16, 64, 196, 1296, 3600, 35344, 1397124, 4804864, 213218404, 2754990144, 9976014400, 133023596176, 6663770519184, 342723467635264, 1281107924034624, 67756702226982976, 963748303995476224, 3643830108147610000, 198705767966065582336, 2876682497805092456704

Offset: 1

N. J. A. Sloane, May 04 2000

M. Klin, V. A. Liskovets and R. Poeschel, Analytical enumeration of circulant graphs with prime-squared vertices, Sem. Lotharingien de Combin., B36d, 1996, 36 pages.

Cf. A038781, A038783.

a(p^2) = A049287(p)^2.

More terms from Valery A. Liskovets, May 09 2001

More terms and offset corrected by Sean A. Irvine, Feb 14 2021

cp's OEIS Frontend

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

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A038783 An intermediate sequence for nonisomorphic circulant undirected p^2-graphs, indexed by odd primes p.

Views

Author

Keywords

Links

Crossrefs

Formula

Extensions

A038784 An intermediate sequence for nonisomorphic circulant undirected p^2-graphs, indexed by odd primes p.

Views

Author

Keywords

Links

Crossrefs

Formula

Extensions