A trail is a walk v_0, e_1, v_1, ..., v_k with no repeated edge. The length of a trail is its number of edges.

A u,v-trail is a trail with first vertex u and last vertex v, where u and v 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

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West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, p. 20, 2000.

Cite this as:

Weisstein, Eric W. "Trail." From MathWorld--A Wolfram Web Resource.

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