The order of a graph is the number of vertices in ; it is denoted by . The same notation is used for the number of elements (cardinality) of a set. Thus, . We write for an arbitrary graph of order n. Similarly, 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.