A060966 Number of nonisomorphic circulant oriented graphs (i.e., Cayley graphs for the cyclic group) of order n.

1, 1, 2, 2, 3, 5, 6, 7, 16, 21, 26, 64, 63, 125, 276

Offset

1,3

Comments

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

I am unable to reproduce these results except most notably for n prime or prime squared. If anyone is able to get a(8)=7 it would be appreciated if you could let me know how or add an example. For a(8), I initially get 10 distinct step sets (up to Cayley isomorphism) which reduce to 9 after graph isomorphism testing but that is still too high. The step sets I have are {}, {1}, {2}, {1,2}, {1,-2}, {1,3}, {1,-3}, {1,2,3}, {1,2,-3}, {1,-2,-3}. After constructing the circulant graphs and testing for isomorphisms {1,2,-3} and {1,-2,-3} combine into a single class. Note that a step of 4 is not possible since this always violates the orientation requirement. Is there another way of looking at this problem, is there another kind of reduction or have I made a logical mistake? Other values I cannot reproduce include a(12) and a(15). - Andrew Howroyd, Apr 30 2017

Links

Table of n, a(n) for n=1..15.

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

Crossrefs

Cf. A049297, A056391, A283189.

Sequence in context: A035541 A187502 A236970 * A135279 A035631 A050046

Adjacent sequences: A060963 A060964 A060965 * A060967 A060968 A060969

Keyword

nonn,more

Author

Valery A. Liskovets, May 09 2001

Status

approved