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<record version="5" id="2762">
 <title>order (of a graph)</title>
 <name>OrderOfAGraph</name>
 <created>2002-03-07 11:32:58</created>
 <modified>2006-10-13 19:35:10</modified>
 <type>Definition</type>
 <creator id="13753" name="Mathprof"/>
 <author id="13753" name="Mathprof"/>
 <author id="76" name="digitalis"/>
 <classification>
	<category scheme="msc" code="05C99"/>
 </classification>
 <synonyms>
	<synonym concept="order (of a graph)" alias="order"/>
 </synonyms>
 <related>
	<object name="Graph"/>
	<object name="SizeOfAGraph"/>
	<object name="MantelsTheorem"/>
 </related>
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 <content>The \emph{order} of a graph $G$ is the number of vertices in $G$; it is denoted by $|G|$. The same notation is used for the number of elements (cardinality) of a set. Thus, $|G| = |V(G)|$. We write $G^n$ for an \emph{arbitrary graph of order n}. Similarly, $G(n,m)$ denotes an \emph{arbitrary graph of order n and size m}.


\footnotesize{Adapted with permission of the author from \emph{\PMlinkescapetext{Modern Graph Theory}} by B\'{e}la Bollob\'{a}s, published by Springer-Verlag New York, Inc., 1998.}</content>
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