# 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.

Title neighborhood (of a vertex) NeighborhoodofAVertex 2013-03-22 11:58:03 2013-03-22 11:58:03 digitalis (76) digitalis (76) 10 digitalis (76) Definition msc 05C99 neighborhood Graph