The skeleton graphs of the Johnson solids are polyhedral graphs which may be termed "Johnson skeleton graphs."
Special cases are summarized in the following table.
The Johnson skeleton graphs 
and 
are minimal unit-distance
forbidden graphs.
The skeleton of the gyroelongated pentagonal pyramid 
appeared in Zaks (1976) and was used by Owens (1980)
in the construction of a 76-node polyhedral quintic nonhamiltonian graph (though
neither author identified the graph as the skeleton
of a particular polyhedron).
An unrelated family of of graphs known as Johnson graphs 
are defined as graphs whose vertices
given by the k-subsets of 
, with two vertices connected iff
their intersection has size 
.
