A critical nonplanar graph is a nonplanar graph 
for which 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.
The Möbius ladders are critical nonplanar graphs.
Critical nonplanar graphs are implemented in the Wolfram Language as GraphData["CriticalNonplanar"].
The numbers of nonisomorphic critical nonplanar simple graphs on 
, 2, ... vertices are 0,
0, 0, 0, 1, 8, 40, 258, ... (OEIS A158922),
the first few of which are illustrated above.
