Wells graph

Wells graph
Wells graph
Vertices	32
Edges	80
Radius	4
Diameter	4
Girth	5
Automorphisms	1920
Chromatic number	4
Chromatic index	5
Queue number	3
Properties	Distance regular; Hamiltonian
	Table of graphs and parameters

The Wells graph is the unique distance-regular graph with intersection array $\{5,4,1,1;1,1,4,5\}.$ ^[1]

Its spectrum is $5^{1}{\sqrt {5}}^{8}1^{1}0(-{\sqrt {5}})^{8}(-3)^{5}$ . Its queue number is 3 and an upper bound on its book thickness is 5.^[2]

References

↑ Brouwer, A. E.; Cohen, A. M.; Neumaier, A. (1989), Distance-Regular Graphs, Springer-Verlag, Theorem 9.2.9
↑ Jessica Wolz, Engineering Linear Layouts with SAT. Master Thesis, University of Tübingen, 2018

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