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.