Wells graph

Wells graph
Wells graph
	File:Wells graph.svg
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 $5^{1} {\sqrt{5}}^{8} 1^{10} (- \sqrt{5})^{8} (- 3)^{5}$ . Its queue number is 3 and an upper bound on its book thickness is 5.^[2]

References

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^ Jessica Wolz, Engineering Linear Layouts with SAT. Master Thesis, University of Tübingen, 2018