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.