tree in graph theory

树

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

Translation evidence: Literature usage

Meaning in context

A tree is a nonempty connected simple graph containing no cycle; this record restricts to finite trees.

本记录中，树是非空、连通且不含圈的有限简单图。

Example

The graph with edges ab,ac,adab,ac,ad is a tree on four vertices.

Usage and distinctions

A forest need not be connected. A one-vertex graph is a tree even though it has no degree-one leaf.

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Definition sources

  1. Keller and Trotter — Applied Combinatorics (2016)Section 5.1, forest/tree definitions and Proposition 5.11 · Checked 2026-10-14

Translation sources

  1. Reinhard Diestel — 图论，第五版，官方中文目录目录，§1.5「树和森林」（中文名称证据，仅目录） · Checked 2026-10-14
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