# Definition:Graph (Graph Theory)/Vertex

< Definition:Graph (Graph Theory)(Redirected from Definition:Vertex of Graph)

## Contents

## Definition

Let $G = \left({V, E}\right)$ 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 $e$.

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): $\S 1.3$: Graphs - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.21$: Euler ($1707$ – $1783$)