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Quasi-Regular Graph


A quasi-regular graph is a graph such that degree of every vertex is the same delta except for a single vertex whose degree is Delta=delta+1 (Bozóki et al. 2020). Quasi-regular graphs must have an odd number of vertices and an odd minimum vertex degree delta.

Quasi-regular graphs with delta=3, 5, ..., may be called quasi-cubic, quasi-quintic, etc.

Examples of disconnected quasi-regular graphs include the graph unions P_3 union nP_2 and W_5 union K_4, where P_n is a path graph, W_n is a wheel graph, and K_4 is the tetrahedral graph.


See also

Quasi-Cubic Graph, Quasi-Quintic 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.

Cite this as:

Weisstein, Eric W. "Quasi-Regular Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Quasi-RegularGraph.html

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