back to table · edit · history · where entries came from · files · download
1530 bytes, as of the version from 2026-10-25 09:43 (current). Recorded here, not run.
# T481 convention fixed before computation
The quantity is gamma_C = lim (c_n/n!)^(1/n), where c_n counts finite simple labelled planar graphs on {1,...,n}, by vertices. An embedding is not part of the counted graph. Parameter order: class, size, labelling. All rows have size=vertices, labelling=labelled.
Classes, in display order: all, connected, 2-connected, 3-connected, maximal. Connectivity is vertex connectivity. Maximal means no edge can be added on the same vertex set while preserving simplicity and planarity; for n>=4 these are the planar triangulations. Finite exceptional small sizes do not affect growth.
Five rows are selected because unrestricted graphs, their connectivity subclasses, and maximal planar graphs are the basic naturally occurring planar-graph counting problems. The table is not exhaustive over all planar subclasses. It will not store reciprocals or amplitudes as additional quantities.
Sources: Giménez–Noy (JAMS 2009), theorem 1, lemma 4, section 4 and appendix; Giménez–Noy survey section 5 (3-connected constant); Tutte triangulation enumeration (also OEIS A007816). The Giménez–Noy paper identifies a unique root t in (0,1) of Y(t)=1; positive real branches and real logarithms are used throughout.
Numerics: rational endpoint bisection, with signs evaluated in Arb ball arithmetic; ball evaluation of analytic radius formulas. Target 100 significant decimal digits. Exact maximal planar value 256/27. All/connected equality is a theorem, not a reason for declaring repeats.