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, 2, ... 個節點上的數量分別為 1, 0, 0, 1, 2, 0, 0, 10, ... (OEIS A000171)。前幾個分別對應於一個節點的平凡圖，路徑圖 
和圈圖 
。
個頂點的自補圖，對於每個整數 
，都存在長度為 
的圖圈 (Rao 1977; Farrugia 1999, p. 51)。因此，具有 
個頂點的自補圖的圖周長為 
(即，該圖是哈密頓圖), 
, 或 
(Furrigia 1999, p. 51)。
個頂點的自補圖，有 
條邊。由於 
必須能被 4 整除，因此 
或 1 (mod 4)。
中獲得，該多項式源自用於列舉簡單圖數量的 Pólya 列舉定理，為 
。