A trail is a walk 
, 
,
, ..., 
with no repeated edge. The length of a trail is its number
of edges.
A 
-trail is a trail with first vertex
and last vertex 
, where 
and 
are known as the endpoints.
A trail is said to be closed if its endpoints are the same.
For a simple graph (which has no multiple edges), a trail may be specified completely by an ordered list of vertices (West 2000, p. 20).
See also
Circuit, Graph Cycle, Graph Path, Walk
Explore with Wolfram|Alpha
More things to try:
References
West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, p. 20, 2000.
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Trail." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Trail.html