# Definition:Adjacent (Graph Theory)/Vertices/Undirected Graph

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## Definition

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

Two vertices $u, v \in V$ of $G$ are **adjacent** if there exists an edge $e = \set {u, v} \in E$ of $G$ to which they are both incident.

Otherwise they are **non-adjacent**.

## Also known as

**Adjacent** vertices can also be described as **neighboring** (British English spelling: **neighbouring**).

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.3$: Graphs