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DualPlanarGraph[g]

给出平面图 g 的对偶图.

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范例  
基本范例  
范围  
应用  
属性和关系  
可能存在的问题  
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DualPlanarGraph

DualPlanarGraph[g]

给出平面图 g 的对偶图.

更多信息和选项

范例

打开所有单元 关闭所有单元

基本范例  (2)

平面图的对偶图：

Wolfram Language code: GraphData[{"Antiprism", 4}]
Wolfram Language code: DualPlanarGraph[%]

三维 HypercubeGraph 是平面图：

Wolfram Language code: PlanarGraph[HypercubeGraph[3]]
Wolfram Language code: DualPlanarGraph[%]

范围  (4)

DualPlanarGraph 适用于无向图：

Wolfram Language code: DualPlanarGraph[[image]]

有向图：

Wolfram Language code: DualPlanarGraph[[image]]

多图：

Wolfram Language code: DualPlanarGraph[[image]]

混合图：

Wolfram Language code: DualPlanarGraph[[image]]

应用  (1)

将对偶图的顶点划分为两个子集，使得其导出子图都是树：

Wolfram Language code: g = PolyhedronData["Dodecahedron", "Skeleton"];

求 Hamiltonian 圈：

Wolfram Language code: h = First[FindHamiltonianCycle[g]]

对偶图：

Wolfram Language code: dg = DualPlanarGraph[g]

选择 Hamiltonian 圈中的顶点：

Wolfram Language code: coords = GraphEmbedding[g];
Wolfram Language code: p = MeshRegion[coords, Polygon[h[[All, 1]]]];
Wolfram Language code: vert1 = Select[VertexList[dg], RegionWithin[p, MeshRegion[coords, Polygon[#]]]&]
Wolfram Language code: vert2 = Complement[VertexList[dg], vert1]

显示此划分的导出子图：

Wolfram Language code: HighlightGraph[dg, Subgraph[dg, #]& /@ {vert1, vert2}, GraphHighlightStyle -> "Thick"]

属性和关系  (2)

用 PlanarFaceList 获取平面图的面：

Wolfram Language code: PlanarFaceList[[image]]

用 FindPlanarColoring 求平面图的面的着色：

Wolfram Language code: FindPlanarColoring[[image]]

可能存在的问题  (2)

DualPlanarGraph 取决于基于给定布局的面：

Wolfram Language code: Graph[[image], GraphLayout -> "PlanarEmbedding"];
Wolfram Language code: DualPlanarGraph[%]

DualPlanarGraph 取决于基于给定坐标的面：

Wolfram Language code: Graph[[image], VertexCoordinates -> {{0, 0}, {3, 0}, {1, 1}, {0, 3}}];
Wolfram Language code: DualPlanarGraph[%]
Wolfram Research (2021)，DualPlanarGraph，Wolfram 语言函数，https://reference.wolfram.com/language/ref/DualPlanarGraph.html.

文本

Wolfram Research (2021)，DualPlanarGraph，Wolfram 语言函数，https://reference.wolfram.com/language/ref/DualPlanarGraph.html.

CMS

Wolfram 语言. 2021. "DualPlanarGraph." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/DualPlanarGraph.html.

APA

Wolfram 语言. (2021). DualPlanarGraph. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/DualPlanarGraph.html 年

BibTeX

@misc{reference.wolfram_2026_dualplanargraph, author="Wolfram Research", title="{DualPlanarGraph}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/DualPlanarGraph.html}", note=[Accessed: 07-October-2026]}

BibLaTeX

@online{reference.wolfram_2026_dualplanargraph, organization={Wolfram Research}, title={DualPlanarGraph}, year={2021}, url={https://reference.wolfram.com/language/ref/DualPlanarGraph.html}, note=[Accessed: 07-October-2026]}