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.
See also
Cubic Graph, Quasi-Quintic Graph, Quasi-Regular Graph, Regular Graph
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References
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.
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Cite this as:
Weisstein, Eric W. "Quasi-Cubic Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Quasi-CubicGraph.html