一个图是平面的当且仅当它有一个组合对偶图 (Harary 1994, p. 115)。任何平面图都有一个图嵌入，即平面直线嵌入，其中边不相交 (Fáry 1948; Bryant 1989; Skiena 1990, pp. 100 and 251; Scheinerman and Wilf 1994)。
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, 2, ... 个节点的平面图的数量分别为 1, 2, 4, 11, 33, 142, 822, 6966, 79853, ... (OEIS A005470; Wilson 1975, p. 162)，其中前几个如图所示。
算法 (1961; Skiena 1990, p. 247)。可以使用 Wolfram 语言 中的命令测试图的平面性：PlanarGraphQ[g].
是平面的，那么 
至少有一个顶点度 
。如果图 
及其图的补图 
都是平面的，那么 
最多有八个顶点。
时是平面的。完全二部图 
是非平面的。更一般地，Kuratowski 在 1930 年证明，一个图是平面的当且仅当它不包含任何完全图 
或 
的图扩展。
的平面图的数量。
, 2, 3, ...