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 $\mathrm{\Gamma }(x)$. Occasionally one calls $\mathrm{\Gamma }(x)$ the open neighborhood of $x$, and $\mathrm{\Gamma }\cup \{x\}$ 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.