Some identities for enumerators of circulant graphs

Details Some identities for enumerators of circulant graphs Some identities for enumerators of circulant graphs

2001-04-12

arxiv.org/abs/math/0104131v1

J. of Algebr. Combin., v.18:3 (2003), 189-209 (in a revised form)

Mathematics

Combinatorics

17 pages, 3 tables Categories: CO Combinatorics (NT Number Theory) Math Subject Class: 05C30; 05A19; 11A41

Scientific paper

10.1023/B:JACO.0000011937.70237.

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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