## Neighborhood of a Vertex

Consider the following graph:

The set of all vertices in $G$ that are 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

$$ N_{\text{outgoing}}(D) = \{C, E\} $$

$$ N_{\text{incoming}}(D) = \{B\} $$