Nonplanar Graph

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A nonplanar graph is a graph that is not planar. The numbers of simple nonplanar graphs on n=1, 2, ... nodes are 0, 0, 0, 0, 1, 14, 222, 5380, 194815, ... (OEIS A145269), with the corresponding number of simple nonplanar connected graphs being 0, 0, 0, 0, 1, 13, 207, 5143, 189195, ... (OEIS A145270).

The following table summarizes some named nonplanar graphs.

graph G |V(G)|

pentatope graph 5

utility graph 6

16-cell graph 8

Petersen graph 10

Grötzsch Graph 11

Chvatal graph 12

Franklin graph 12

uniquely three-colorable graph 12

Heawood graph 14

Clebsch graph 16

Hoffman graph 16

Möbius-Kantor graph 16

tesseract graph 16

first Blanuša snark 18

second Blanuša snark 18

Pappus graph 18

Robertson graph 19

Desargues graph 20

flower snark J_5 20

Folkman graph 20

24-cell graph 24

25-Grünbaum graph 25

Coxeter graph 28

double star snark 30

Tutte 8-cage 30

Meringer graph 30

Robertson-Wegner graph 30

Thomassen graph 34

Sylvester graph 36

Hoffman-Singleton graph 50

Szekeres snark 50

Gewirtz graph 56

Balaban 10-cage 70

Meredith graph 70

Foster graph 90

Biggs-Smith graph 102

Balaban 11-cage 112

600-cell graph 120

Tutte 12-cage 126

McLaughlin graph 275

120-cell graph 600

See also

Critical Nonplanar Graph, Cubic Nonplanar Graph, Kuratowski Reduction Theorem, Planar Graph

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References

Sloane, N. J. A. Sequences A145269 and A145270 in "The On-Line Encyclopedia of Integer Sequences."

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Nonplanar Graph

Cite this as:

Weisstein, Eric W. "Nonplanar Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NonplanarGraph.html

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