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

Author

Valery A. Liskovets, May 09 2001

Keywords

• nonn
• more

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

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

Crossrefs

Cf. A049297, A056391, A283189.