Definition:Boundary (Graph Theory)

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 $v$:

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