path in a graph

路

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

Other names / variants: simple path

Translation evidence: Literature usage

Meaning in context

In a simple graph, a path is a finite sequence of distinct vertices whose consecutive pairs are edges; its length is the number of consecutive pairs.

简单图中的路是一个顶点不重复的有限序列，连续两点之间都有边；长度为所用边数。

Example

In the graph with edges $ab,bc$, the sequence $(a,b,c)$ is a path of length two.

Usage and distinctions

A walk may repeat vertices; a path may not. This convention admits a one-vertex path of length zero.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Keller and Trotter — Applied Combinatorics (2016)Section 5.1, walk/path definition and path-length convention · Checked 2026-10-14

Translation sources

1. Reinhard Diestel — 图论，第五版，官方中文目录目录，§1.3「路和圈」（中文名称证据，仅目录） · Checked 2026-10-14

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