A nonplanar graph 
is said to be critical nonplanar if the removal of a vertex
results in a planar graph for every vertex
of 
.
Critical nonplanar graphs differ from apex graphs in that an apex graph requires only that there exist at least one vertex whose removal gives a planar graph, while a critical nonplanar graph requires that removal of each vertex gives a planar graph.
Classes of graphs that are critically nonplanar include the Möbius ladder.
Critical nonplanar graphs are implemented in the Wolfram Language as GraphData["CriticalNonplanar"].
The numbers of critical nonplanar simple graphs on 
, 2, ... nodes are 0, 0, 0, 0, 1, 8, 40, 258, ... (OEIS A158922), the first few of which are illustrated
above.
