Neighborhood of a Vertex

  • Define the neighborhood of a vertex.

Consider the following graph:

The set of all vertices in GG adjacent to a vertex vv is called the neighborhood of vv and denoted by N(v)N(v).

Noutgoing(A)={B,C} N_{\text{outgoing}}(A) = \{B, C\}

Nincoming(C)={A,D} N_{\text{incoming}}(C) = \{A, D\}

Exercise Name all the vertices adjacent to vertex DD in two groups – incoming neighbors and outgoing neighbors:

Solution

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

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