

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
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OFFSET

1,3


COMMENTS

These and subsequent values for (twice) squarefree and (twice) primesquared 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


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KEYWORD

nonn,more


AUTHOR



STATUS

approved



