【摘要】 循环图已被用于平行计算，网络等方面．循环图研究的一个基本问题是对互不同构的循环图进行计数．对于给定的一个正整数ｎ，用Ｃ（ｎ，ｋ）表示互不同构的具有几个顶点，度数为ｋ的连通循环图的个数．文中给出了度数为 ４和５的循环图的一般结构，并对ｎ＝ｐａｑｂ（ｐ，ｑ皆为素数，ａ，ｂ＞０），给出了Ｃ（ｎ，４）的计算公式．更多还原

【Abstract】 Circulant graphs have been applied to Ramsey type problem, parallel computing and networks. A basic problem in research of circulant graphs is counting nonisomorphic circulant graphs. Given positive integers n and k, let C(n, k) denote the number of connected and pairwise nonisomorphic circulant graphs having n vertices and valency k. In this paper first we obtain C(n, 5) by using the parameters C(n, 4) and C(n/2, 4). Then we investigate structure of circulant graphs with valency 4 for computing C(n, 4). Finally, as an application of the previous results, we calculate C(n, 4), for n = paqb with p, q primes and a, b≥ 0.更多还原