Definition:Walk (Graph Theory)
A walk on a graph is:
- an alternating series of vertices and edges
- beginning and ending with a vertex
- in which each edge is incident with the vertex immediately preceding it and the vertex immediately following it.
A walk between two vertices $u$ and $v$ is called a $u$-$v$ walk.
That is, it is a walk which ends where it starts.
Also known as
Some sources refer to a walk as a path, and use the term simple path to define what we have here as a path.
- 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): $\S 2.3$: Connected Graphs
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Entry: walk
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: walk (in graph theory)