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.

Title	neighborhood (of a vertex)
Canonical name	NeighborhoodofAVertex
Date of creation	2013-03-22 11:58:03
Last modified on	2013-03-22 11:58:03
Owner	digitalis (76)
Last modified by	digitalis (76)
Numerical id	10
Author	digitalis (76)
Entry type	Definition
Classification	msc 05C99
Synonym	neighborhood
Related topic	Graph