# Definition:Graph (Graph Theory)/Vertex

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## Definition

Let $G = \struct {V, E}$ be a graph.

The **vertices** (singular: **vertex**) are the elements of $V$.

Informally, the **vertices** are the points that are connected by the edges.

## Also known as

When $G$ is a tree, the **vertices** are usually called nodes.

## Also see

If $e \in E$ is an edge joining the **vertex** $u$ to the **vertex** $v$, $u$ and $v$ are called the endvertices of $e$.

## Linguistic Note

The plural of **vertex** is **vertices**.

The word **vertex** is Latin for **peak**, from which the irregular plural form.

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.3$: Graphs - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.21$: Euler ($\text {1707}$ – $\text {1783}$) - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**vertex**(of a graph)