# Wells graph

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

Wells graph
Vertices32
Edges80
Diameter4
Girth5
Automorphisms1920
Chromatic number4
Chromatic index5
Queue number3
PropertiesDistance regular
Hamiltonian
Table of graphs and parameters

Its spectrum is ${\displaystyle 5^{1}{\sqrt {5}}^{8}1^{1}0(-{\sqrt {5}})^{8}(-3)^{5}}$. Its queue number is 3 and its upper bound on the 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