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
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

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]