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.

Bozóki S.; Szadoczki, Z.; and Tekile, H. A. "Filling in Pattern Designs for Incomplete Pairwise Comparison Matrices: (Quasi-)Regular
Graphs With Minimal Diameter." 13 May 2020. https://arxiv.org/abs/2006.01127.