# 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** $G$.

## Also see

## Source of Name

This entry was named for Leonhard Paul Euler.

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): $\S 3.1$: The Königsberg Bridge Problem: An Introduction to Eulerian Graphs - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.21$: Euler ($1707$ – $1783$)