Definition:Neighborhood (Graph Theory)
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This page is about Neighborhood in the context of Graph Theory. For other uses, see Neighborhood.
Definition
Let $G = \struct {V, E}$ be a graph.
Let $v \in V$ be a vertex of $G$.
The neighborhood of $v$ in $G$ is:
- $\map {\Gamma_G} v = \set {u \in V : u v \in E}$
That is, it is the set of all vertices which are adjacent to $v$.
Internationalization
Neighborhood is translated:
In Dutch: | nabuurschap | |||
In French: | voisinage |
Linguistic Note
The UK English spelling of neighborhood is neighbourhood.