Topic summary
Adjacent vertices
Extracted from the Wikipedia article Neighbourhood (graph theory).
The neighbourhood is often denoted by or (when the graph is unambiguous) . The same neighbourhood notation may also be used to refer to the set of adjacent vertices rather than the corresponding induced subgraph. The neighbourhood described above does not include v itself, and is more specifically the open neighbourhood of v; it is also possible to define a neighbourhood in which v itself is included, called the closed neighbourhood of v and denoted by . When stated without any qualification, a neighbourhood is assumed to be open.
![{\displaystyle N_{G}[v]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/70d0730ce5bb03368f6dda06206b1e59278c8bf4)