Planar Graph Growth Constants

Steven Finch August 25, 2004 A graph of order  consists of a set of  vertices (points) together with a set of edges (unordered pairs of distinct points). Note that loops and multiple parallel edges are automatically disallowed. Two vertices joined by an edge are called adjacent. Two graphs  and  are isomorphic if there is a one-to-one map from the vertices of  to the vertices of  that preserves adjacency (see Figure 1). Diagrams for all non-isomorphic graphs of order ≤ 7 appear in [1]. A graph is connected if, for any two distinct vertices  and , there is a sequence of adjacent vertices 0, 1, ...,  such that 0 =  and  =  (see Figure 2). The generating function for graphs [2]