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