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Homeneighborhood (of a vertex)

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# neighborhood (of a vertex)

For a graph $G$, the set of vertices adjacent to a vertex $x\in G$, the *neighborhood* of $x$, is denoted by $\Gamma(x)$. Occasionally one calls $\Gamma(x)$ the *open* neighborhood of $x$, and $\Gamma\cup\{x\}$ the *closed* neighborhood of $x$.

Adapted with permission of the author from *Modern Graph Theory* by Béla Bollobás, published by Springer-Verlag New York, Inc., 1998.

Keywords:

vertex, graph

Related:

Graph

Synonym:

neighborhood

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

05C99*no label found*

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