标题： 一些关于循环图计数器的恒等式 显示英文标题

标题： Some identities for enumerators of circulant graphs

摘要： 我们通过分析建立了几个新的恒等式，连接了不同类型的循环图的计数器，这些循环图的阶数为质数、两倍质数和质数平方。 特别是，证明了质数阶的无向循环图的数量与无向自补循环图的数量的半和等于相同阶的有向自补循环图的数量。 关键词：循环图；循环指标；循环群；几乎翻倍的质数； 坎宁安链；自补图；竞赛图；混合图 显示英文摘要

摘要： 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