The Number of Labeled 2-Connected Planar Graphs

Edward A. Bender, Zhicheng Gao, Nicholas C. Wormald


We derive the asymptotic expression for the number of labeled 2-connected planar graphs with respect to vertices and edges. We also show that almost all such graphs with $n$ vertices contain many copies of any fixed planar graph, and this implies that almost all such graphs have large automorphism groups.

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