A quasi-qunitic 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), where 
. Such graphs must have an odd
number of vertices.
All quasi-quintic graphs on at least 10 nodes or fewer are connected, and the numbers of quasi-quintic graphs on 
, 2, ... nodes are 0, 0, 0, 0, 0, 0, 1, 0, 20, 0, .... Examples
are summarized in the following table and illustrated above.
 | examples |
| 7 | Túran graph  |
| 9 | Harary graph  |
