# Definition:Boundary (Graph Theory)

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*This page is about the boundary of a vertex in the context of Graph Theory. For other uses, see Boundary.*

## Definition

### Simple Graph

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

Let $v \in V$ be a vertex of $G$.

Then the **boundary** of $v$ is the set of all vertices of $G$ which are adjacent to $v$:

- $\map B v = \set {u \in V: \set {u, v} \in E}$