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 ${\displaystyle \{5,4,1,1;1,1,4,5\}.}$ ^[1]

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

References

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

External links

• A.E. Brouwer's website: The Armanios-Wells graph