The graph neighborhood of a vertex v in a graph is the set of all the vertices adjacent to v including v itself. More generally, the ith neighborhood of v is the set of all vertices that lie at the distance i from v. The subgraph induced by the neighborhood of a graph from vertex v is called the neighborhood graph. Note that while "graph neighborhood" generally includes vertices adjacent to v together with the vertex v itself, the term "graph neighbors" generally means vertices adjacent to v excluding v itself (e.g., Brouwer et al. 1989), so some care is needed when encountering these terms.

dominating set | graph distance graph | irredundant set | local graph | neighborhood | neighborhood graph