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.
We guarantee you’ll find the right tutor, or we’ll cover the first hour of your lesson.