Definition:Path (Graph Theory)
A path between two vertices $u$ and $v$ is called a $u$-$v$ path.
This subgraph itself is also referred to as a path.
Also known as
Some sources call this a simple path, and use the term path to define what we have here as a walk.
A path in a graph $G$ can be referred to as a $G$-path.
- Definition:Cycle (Graph Theory): a closed path: that is, a path in which the first and last vertices are the same.
By this definition it would appear that a path is automatically a trail, because if an edge were to be retraced in any walk, then the vertices at either end of it would necessarily be visited more than once.
Hence the insistence that a path is a type of trail.
- 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): $\S 2.3$: Connected Graphs
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Entry: walk
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Entry: walk
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: path (in a graph)