A quasi-cubic graph is a quasi-regular graph, i.e., a graph such that degree of every vertex is the same 
except for a single vertex whose degree is 
(Bozóki et al. 2020), with 
.
The numbers of connected quasi-quintic graphs on 
, 2, ... nodes are 0, 0, 0, 0, 1, 0, 4, 0, 27, 0, ... and
the numbers of not-necessarily connected quasi-quintic graphs on 
, 2, ... nodes are 0, 0, 0, 0, 1, 0, 4, 0, 28, 0, .... The
sole disconnected quasi-cubic graph on 10 nodes or fewer is the graph
union 
of the 5-wheel graph and the tetrahedral
graph. Examples are illustrated above and are summarized in the table below.
 | quasi-cubic graphs |
| 5 | wheel graph  |
| 7 | Harary graph  , Moser spindle |
| 9 | Harary
graph  ,
 -unit
distance-forbidden graph,  |
