connected graph

连通图

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

Translation evidence: Literature usage

Meaning in context

A nonempty finite simple graph is connected when each pair of vertices is joined by a path.

非空有限简单图中，任意两点之间都存在路时，称该图为连通图。

Example

A single vertex with no edges is connected; two isolated vertices are not.

Usage and distinctions

This record excludes the null graph by convention. Connected does not mean complete: a three-vertex path is connected.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Keller and Trotter — Applied Combinatorics (2016)Section 5.1, connected/disconnected graph and component definitions · Checked 2026-10-14

Translation sources

  1. 电子科技大学教学平台 — 《图论及其应用》习题课教材（片段）PDF p.1，习题1，第1题「n阶连通图」（名称证据） · Checked 2026-10-14
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