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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


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.


Cf. A049297, A056391, A283189.

Sequence in context: A035541 A187502 A236970 * A172993 A135279 A035631

Adjacent sequences:  A060963 A060964 A060965 * A060967 A060968 A060969




Valery A. Liskovets, May 09 2001



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Last modified February 17 16:15 EST 2018. Contains 299296 sequences. (Running on oeis4.)