Neighbourhood of a vertex
Neighbourhood of a vertex --- окрестность вершины.
For each vertex the set of vertices which are adjacent to . The other name is open neighbourhood. The closed neighbourhood is .
For disjoint subsets and of , we define to be the set of all edges that join a vertex of and a vertex of . Furthermore, for , we define the private neighbourhood of in to be the set of vertices in that are adjacent to but to no other vertex of ; that is, .
Given a digraph , let be distinct vertices in . If there is an arc from to , then we say that dominates and write and call (respectively, ) an out-neighbour (out-neighborhood) (respectively, an in-neighbour (in-neighborhood)) of (respectively, ). We let denote the set of out-neighbours, respectively, the set of in-neighbours of in . Define to be .
is an out-semicomplete digraph (in-semicomplete digraph) if has no pair of non-adjacent vertices with a common in-neighbour or a common out-neighbour. is a locally semicomplete digraph if is both out-semicomplete and in-semicomplete.