Nonplanar Graph

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

The following table summarizes some named nonplanar graphs.

graph
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	20
Folkman graph	20
McGee graph	24
24-cell graph	24
25-Grünbaum graph	25
Doyle graph	27
Coxeter graph	28
double star snark	30
Foster cage	30
Tutte 8-cage	30
Meringer graph	30
Robertson-Wegner graph	30
Wong graph	30
Dyck graph	32
Wells graph	32
Thomassen graph	34
Sylvester graph	36
Hoffman-Singleton graph	50
Szekeres snark	50
Gray graph	54
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