induced subgraph

导出子图

Combinatorics · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

For a simple graph G=(V,E) and W ⊆ V, the induced subgraph G[W] has vertex set W and exactly the edges of E whose two endpoints belong to W.

对简单图 G=(V,E) 和 W⊆V，导出子图 G[W] 的顶点集是 W，边恰为 E 中两端都在 W 内的边。

Example

In a triangle, the induced subgraph on any two vertices is K2K_2.

Usage and distinctions

This record uses the source’s term 导出子图. Deleting an edge while keeping both endpoints usually stops the result being induced.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Keller and Trotter — Applied Combinatorics (2016)Section 5.1, induced subgraph definition · Checked 2026-10-14

Translation sources

  1. 海南大学学报自然科学版 — 对于2树和3树的一个刻画p.111，正文开篇，G[X]的「导出子图」记号（名称证据） · Checked 2026-10-14
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