%0 Report %1 klin/liskovets/poeschel:2003 %A Klin, Mikhail %A Liskovets, Valery %A Pöschel, Reinhard %D 2003 %K 2003 poeschel preprint %N MATH-AL-07-2003 %T On the Analytic Enumeration of Circulant Graphs %X We systematize, extend, and survey results of the analytical (i.e. represented by formulae) exact enumeration of circulant graphs. A convenient unified approach to counting various types of circulant graphs possessing the so-called Cayley isomorphism (CI) property is proposed. The results are represented uniformly in terms of well-specified Abelian permutation groups and their cycle index polynomials. This technique comprises mostly square-free orders, but it may be generalized to prime-squared (and also prime-power) orders, due to an isomorphism criterion for circulants of these orders. In the last section we provide vast numerical tables and suggest two conjectures.

@techreport{klin/liskovets/poeschel:2003, abstract = {We systematize, extend, and survey results of the analytical (i.e. represented by formulae) exact enumeration of circulant graphs. A convenient unified approach to counting various types of circulant graphs possessing the so-called Cayley isomorphism (CI) property is proposed. The results are represented uniformly in terms of well-specified Abelian permutation groups and their cycle index polynomials. This technique comprises mostly square-free orders, but it may be generalized to prime-squared (and also prime-power) orders, due to an isomorphism criterion for circulants of these orders. In the last section we provide vast numerical tables and suggest two conjectures.}, added-at = {2009-10-27T17:34:10.000+0100}, author = {Klin, Mikhail and Liskovets, Valery and Pöschel, Reinhard}, biburl = {https://www.bibsonomy.org/bibtex/2d91b05f17c2c502442b1ca4645710b2f/algebradresden}, institution = {TU Dresden}, interhash = {186abe4e298705bfb272eaccb879ffd2}, intrahash = {d91b05f17c2c502442b1ca4645710b2f}, keywords = {2003 poeschel preprint}, msc = {05C30, 05C25, 05C20}, number = {MATH-AL-07-2003}, timestamp = {2010-01-27T17:46:55.000+0100}, title = {On the Analytic Enumeration of Circulant Graphs}, type = {Preprint}, year = 2003 }