a first vertex but no last vertex.
* A trail is a walk in which all edges are distinct.
* A path is a trail in which all vertices (and therefore also all edges) are distinct.

If is a finite walk with vertex sequence then is said to be a walk from to . Similarly for a trail or a path. If there is a finite walk between two distinct vertices then there is also a finite trail and a finite path between them.

Some authors do not require that all vertices of a path be distinct and instead use the term simple

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