Walk

Builds on Graph

Definition

Let $G$ be a graph, let $k$ be a natural number, and let $u, v$ be vertices of $G$ . A walk of length $k$ from $u$ to $v$ is a sequence of vertices $(w_0, w_1, \dots, w_k)$ with $w_0 = u$ , $w_k = v$ , and $w_{i-1} \sim w_i$ for $1 \le i \le k$ . Its edges are the edges $w_{i-1} w_i$ .

Remarks

A walk may repeat vertices and edges. A walk of length $0$ is a single vertex. A trail has no repeated edge, and a path has no repeated vertex. A walk is closed if $u = v$ .

Reading path

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Show the path as a graph

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Graph definition
Walk definition

Where this leads

55 pages build on this one.

Tag	`0VJZM0F9YM`
URI	`m2://0VJZM0F9YM`
Kind	definition
Writing	W0 stub
MSC	05C38
Defines	Walk
Uses	Graph

Walk

Definition

Remarks

Reading path

Where this leads

Further reading

What this page needs for W1

What links here

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