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# order (of a graph)

The *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 *arbitrary graph of order n*. Similarly, $G(n,m)$ denotes an *arbitrary graph of order n and size m*.

Adapted with permission of the author from *Modern Graph Theory* by Béla Bollobás, published by Springer-Verlag New York, Inc., 1998.

Related:

Graph, SizeOfAGraph, MantelsTheorem

Synonym:

order

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

05C99*no label found*

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