neighborhood (of a vertex)NeighborhoodOfAVertex2001-11-12 20:04:322002-03-07 11:57:27Definitionvertexgraph\usepackage{amssymb}
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\usepackage{xypic}For a graph $G$, the set of vertices adjacent to a vertex $x \in G$, the \emph{neighborhood} of $x$, is denoted by $\Gamma(x)$. Occasionally one calls $\Gamma(x)$ the \emph{open} neighborhood of $x$, and $\Gamma \cup \{x\}$ the \emph{closed} neighborhood of $x$.
\footnotesize{Adapted with permission of the author from \emph{Modern Graph Theory} by B\'{e}la Bollob\'{a}s, published by Springer-Verlag New York, Inc., 1998.}