Definition:Boundary (Graph Theory)

Simple Graph
Let $G = \left({V, E}\right)$ 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 $v$:
 * $B \left({v}\right) = \left\{{u \in V: \left\{{u, v}\right\} \in E}\right\}$