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Some identities for enumerators of circulant graphs

Valery A. Liskovets
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Abstract

We establish analytically several new identities connecting enumerators of different types of circulant graphs of prime, twice prime and prime-squared orders. In particular, it is shown that the semi-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. Keywords: circulant graph; cycle index; cyclic group; nearly doubled primes; Cunningham chain; self-complementary graph; tournament; mixed graph

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Valery A. Liskovets. 2001-04-12. Some identities for enumerators of circulant graphs. https://doi.org/10.1023/b%3Ajaco.0000011937.70237.0b

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