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, 2, ... 的單圖圖的數量是 1, 2, 4, 11, 28, 72, 170, 407, 956, 2252 ... (OEIS A122423)，其中連通圖的數量是 1, 1, 2, 6, 16, 42, 96, 234, 546, 1292, ... (OEIS A365548)。在所有節點數為 
的連通圖中，具有不同度序列的連通圖的數量，對於 
, 2, ... 是 1, 1, 1, 2, 6, 17, 45, 99, 238, 549, 1296, ... (OEIS A309757)。
和 
，它們共享度序列 
。
是單圖圖，則其圖補圖 
也是單圖圖 (Barrus et al. 2023)。
是單圖圖 當且僅當 其 Tyshkevich 分解的每個分量都是單圖圖 (Tyshkevich 2000, Barrus et al. 2023)。
、空圖 
、梯子階圖 
、雞尾酒會圖 
和圈圖 
(Johnson 1975, Koren 1976, Tyshkevich 2000)。