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皇后图 
是一个具有 
个顶点的图，其中每个顶点代表一个 
棋盘上的一个方格，每条边对应于皇后的一次合法移动。
-皇后图具有良好的嵌入，如上图所示。一般来说，顶点对应于棋盘方格的嵌入，当绘制为直线时，其边会与其他边重叠，唯一的非平凡例外是 
-皇后图。
"Queen", 
m, n
].
-皇后图
-
-皇后图
-皇后图
-
-皇后图，它与 四面体图 
同构。
, 
, 和 
。
的 4-圈数量的闭合公式为
-皇后图，当 
, 3, ... 时，哈密顿圈的数量分别为 6, 3920, ... (OEIS A158663)，相应的 哈密顿路径 的数量分别为 24, 45856, ... (OEIS A158664)。
-皇后图的每一行和每一列都是一个 
-团，因此这些图的 色数 至少为 
。事实上，当 
时，可以证明 
种颜色就足够了。实际上，对于 
, 3, ...，色数分别为 4, 5, 5, 5, 7, 7, 9, 10, 11, 11, 12, 13, ... (OEIS A088202)。
中 
或 
至少有一个是偶数时 (J. DeVincentis 和 S. Wagon，私人通信，11 月 13-14 日，2011 年) 以及当 
和 
均为奇数且 
时 (S. Wagon，私人通信，2015 年 12 月 9 日)，皇后图 
为奇数且 
时，皇后图显然为 2 类 (S. Wagon，私人通信，2015 年 12 月 9 日)，这仅留下 
为奇数且 
的情况有待研究。
Graph Coloring Problems." J. Heuristics 10, 407-413, 2004.Wagon, S. "Graph Theory Problems from Hexagonal and Traditional Chess." College Math. J. 45, 278-287, 2014.