The OEIS is supported by the many generous donors to the OEIS Foundation.



Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A060966 Number of nonisomorphic circulant oriented graphs (i.e., Cayley graphs for the cyclic group) of order n. 3
1, 1, 2, 2, 3, 5, 6, 7, 16, 21, 26, 64, 63, 125, 276 (list; graph; refs; listen; history; text; internal format)
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
V. A. Liskovets, Some identities for enumerators of circulant graphs, arXiv:math/0104131 [math.CO], 2001.
Sequence in context: A035541 A187502 A236970 * A135279 A035631 A050046
Valery A. Liskovets, May 09 2001

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 3 21:20 EST 2023. Contains 367540 sequences. (Running on oeis4.)