# Definition:Eulerian Trail

## Definition

An Eulerian trail is a trail $T$ that passes through every vertex of a graph $G$ and uses every edge of $G$ exactly once.

## Also known as

An Eulerian trail is also known as an Eulerian path by treatments which define a path how $\mathsf{Pr} \infty \mathsf{fWiki}$ defines a trail.

Some sources use the term Euler path or Euler trail.

An Eulerian trail is said to traverse $G$.

## Source of Name

This entry was named for Leonhard Paul Euler.