Geodesic
Some identities for enumerators of circulant graphs
Journal of Algebraic Combinatorics, Tome 18 (2003) no. 3, pp. 189-209.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We establish analytically several new identities connecting enumerators of different types of circulant graphs mainly of prime, twice prime and prime-squared orders. In particular, it is shown that the half-sum of the number of undirected circulants and the number of undirected self-complementary circulants of prime order is equal to the number of directed self-complementary circulants of the same order. Several identities hold only for prime orders $p$ such that $( p + 1)/2$ is also prime. Some conjectured generalizations and interpretations are discussed.
Classification : 05C30,, 05A19,, 11A41
Keywords: cycle index, cyclic group, nearly doubled primes, cunningham chain, self-complementary graph, regular tournament 
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     title = {Some identities for enumerators of circulant graphs},
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Liskovets, Valery. Some identities for enumerators of circulant graphs. Journal of Algebraic Combinatorics, Tome 18 (2003) no. 3, pp. 189-209. http://geodesic.mathdoc.fr/item/JAC_2003__18_3_a3/