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EdgeTransitiveGraphQ[g]

如果图 g 是边传递图，给出 True，否则给出 False.

更多信息
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基本范例  
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EdgeTransitiveGraphQ

EdgeTransitiveGraphQ[g]

如果图 g 是边传递图，给出 True，否则给出 False.

更多信息

  • 对于图 g 中的任意边 e1 和 e2，如果存在一个 g 的自同构，将 e1 映射到 e2，则图 g 是边传递的.
  • EdgeTransitiveGraphQ 通常用于测试图中的所有边是否具有相同的邻域.

范例

打开所有单元 关闭所有单元

基本范例  (2)

测试图是否是边传递的：

Wolfram Language code: CompleteGraph[3]
Wolfram Language code: EdgeTransitiveGraphQ[%]

轮图不是边传递的：

Wolfram Language code: WheelGraph[5]
Wolfram Language code: EdgeTransitiveGraphQ[%]

范围  (7)

测试无向图：

Wolfram Language code: EdgeTransitiveGraphQ[[image]]

有向图：

Wolfram Language code: EdgeTransitiveGraphQ[[image]]

多重图：

Wolfram Language code: EdgeTransitiveGraphQ[[image]]

混合图：

Wolfram Language code: EdgeTransitiveGraphQ[[image]]

已标注的图：

Wolfram Language code: EdgeTransitiveGraphQ[[image]]

对于不是边传递图的任何内容，EdgeTransitiveGraphQ 给出 False：

Wolfram Language code: EdgeTransitiveGraphQ[a]

EdgeTransitiveGraphQ 适用于大图：

Wolfram Language code: GridGraph[{10, 10, 10, 10}];
Wolfram Language code: EdgeTransitiveGraphQ[%]//Timing

应用  (1)

从 GraphData 生成一组边传递图：

Wolfram Language code: GraphData["EdgeTransitive"]//Short

查看是否为边传递图：

Wolfram Language code: EdgeTransitiveGraphQ[GraphData[#]] & /@ Take[%, 5]

属性和关系  (5)

连通边传递图要么是顶点传递图要么是二分图：

Wolfram Language code: data = Intersection[GraphData["EdgeTransitive"], GraphData["Connected"]]; graphs = GraphData[#] & /@ Take[data, {6, 11}]
Wolfram Language code: (VertexTransitiveGraphQ[#] || BipartiteGraphQ[#])& /@ graphs

用 VertexTransitiveGraphQ 测试连通图是否是边传递的：

Wolfram Language code: g = GraphData[{"Arrangement", {5, 2}}]
Wolfram Language code: VertexTransitiveGraphQ[LineGraph[g]]
Wolfram Language code: EdgeTransitiveGraphQ[g]

边传递图不一定是顶点传递图：

Wolfram Language code: g = GraphData["GrayGraph"]
Wolfram Language code: EdgeTransitiveGraphQ[g]
Wolfram Language code: VertexTransitiveGraphQ[g]

边传递图的顶点连通度等于最小的顶点度：

Wolfram Language code: g = [image];
Wolfram Language code: EdgeTransitiveGraphQ[g]
Wolfram Language code: VertexConnectivity[g] == Min[VertexDegree[g]]

边传递图包括 CompleteGraph：

Wolfram Language code: Table[CompleteGraph[n], {n, 3, 6}]
Wolfram Language code: EdgeTransitiveGraphQ /@ %

完全二分图：

Wolfram Language code: Table[CompleteGraph[{n, n}], {n, 3, 6}]

CycleGraph：

Wolfram Language code: Table[CycleGraph[n], {n, 3, 6}]
Wolfram Language code: EdgeTransitiveGraphQ /@ %

Gray 图：

Wolfram Language code: GraphData["GrayGraph"]
Wolfram Language code: EdgeTransitiveGraphQ[%]
Wolfram Research (2021)，EdgeTransitiveGraphQ，Wolfram 语言函数，https://reference.wolfram.com/language/ref/EdgeTransitiveGraphQ.html.

文本

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_edgetransitivegraphq, author="Wolfram Research", title="{EdgeTransitiveGraphQ}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/EdgeTransitiveGraphQ.html}", note=[Accessed: 15-September-2026]}

BibLaTeX

@online{reference.wolfram_2026_edgetransitivegraphq, organization={Wolfram Research}, title={EdgeTransitiveGraphQ}, year={2021}, url={https://reference.wolfram.com/language/ref/EdgeTransitiveGraphQ.html}, note=[Accessed: 15-September-2026]}