# Definition:Eulerian Graph

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## Definition

A loop-multigraph or loop-multidigraph is called **Eulerian** if and only if it contains an Eulerian circuit.

An **Eulerian graph** is also, by definition, traversable.

## Also known as

An **Eulerian graph** is also called a **unicursal graph**.

## Also see

- Results about
**Eulerian graphs**can be found here.

## Source of Name

This entry was named for Leonhard Paul Euler.

## Linguistic Note

After the pronunciation of Euler as **Oiler**, the word **Eulerian** is pronounced something like **oy- leer-ee-an**.

The term **unicursal**, derives from the prefix **uni-**, an adjectival form of **one** and **cursal**, which derives from the Latin **cursor**, meaning **runner**.

Hence a **unicursal graph** can be understood as a graph which can be drawn in a **single run**.

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): $\S 3.1$: The Königsberg Bridge Problem: An Introduction to Eulerian Graphs: Theorem $3.1$ - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**Eulerian graph** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**Eulerian graph**