V2EX complement graph

Complement Graph

释义 Definition

补图(complement graph):在图论中,给定一个(通常指简单无向图)\(G=(V,E)\),它的补图 \(\overline{G}\) 具有相同的顶点集 \(V\),并且对任意两个不同顶点 \(u,v\),当且仅当 \(uv\notin E\) 时,\(\overline{G}\) 中存在边 \(uv\)。直观地说:把原图中没有连边的点对都连起来,把已有的边都去掉。(通常不考虑自环与重边。)

发音 Pronunciation (IPA)

/kmplmnt rf/; /kmplmnt rf/

例句 Examples

The complement graph has an edge wherever the original graph does not.
补图会在原图没有边的地方补上一条边。

In many proofs, we analyze a graph and its complement graph to compare clique and independent set properties.
在许多证明中,我们会同时分析一个图及其补图,以比较团(clique)与独立集(independent set)的性质。

词源 Etymology

complement 源自拉丁语 complementum,含义是“补足、补充”;在数学里引申为“对某个结构取缺失的部分”。graph 源自希腊语 graphein(“书写、描绘”),在现代数学中指用点和边来“画出/表示”关系的结构。因此 complement graph 字面可理解为“把图中缺的关系补全后得到的图”。

相关词 Related Words

文学与著作 Literary Works

  • Graph Theory Reinhard Diestel(常在讨论基本概念与性质时使用“complement”/“complement graph”)
  • Introduction to Graph Theory Douglas B. West(补图常用于例题与证明,如团与独立集的对偶关系)
  • Graph Theory J. A. Bondy & U. S. R. Murty(补图作为基础工具出现在多处定理与练习中)
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