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# Planar Connected Graph

A planar connected graph is a graph which is both planar and connected. The numbers of planar connected graphs with , 2, ... nodes are 1, 1, 2, 6, 20, 99, 646, 5974, 71885, ... (OEIS A003094; Steinbach 1990, p. 131). A subset of planar 3-connected graphs are called polyhedral graphs.

The following table gives the numbers of planar connected graphs having minimal degrees of at least .

 OEIS , 2, 3, ... 2 A054381 0, 0, 1, 3, 10, 49, 332, ...

The numbers of planar connected graphs with , 2, ... edges are 1, 1, 3, 5, 12, 30, 79, 227, 709, 2318, ... (OEIS A046091).

Connected Graph, Planar Graph, Polyhedral Graph, Polynema

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## References

McKay, B. "Planar Graphs." http://cs.anu.edu.au/~bdm/data/graphs.html.Sloane, N. J. A. Sequences A003094/M1652, A046091, and A054381 in "The On-Line Encyclopedia of Integer Sequences."Steinbach, P. Field Guide to Simple Graphs. Albuquerque, NM: Design Lab, 1990.

## Referenced on Wolfram|Alpha

Planar Connected Graph

## Cite this as:

Weisstein, Eric W. "Planar Connected Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PlanarConnectedGraph.html