Neighborhood of a Vertex
- Define the neighborhood of a vertex.
Consider the following graph:
The set of all vertices in $G$ adjacent to a vertex $v$ is called the neighborhood of $v$ and denoted by $N(v)$.
$$ N_{\text{outgoing}}(A) = \{B, C\} $$
$$ N_{\text{incoming}}(C) = \{A, D\} $$
Exercise Name all the vertices adjacent to vertex $D$ in two groups – incoming neighbors and outgoing neighbors:
Solution
$$ N_{\text{outgoing}}(D) = \{C, E\} $$
$$ N_{\text{incoming}}(D) = \{B\} $$