The Wells graph is the unique distance-regular graph with intersection array

{ 5 , 4 , 1 , 1 ; 1 , 1 , 4 , 5 } .

{\displaystyle \{5,4,1,1;1,1,4,5\}.}

[1] Its spectrum is

Its queue number is 3 and an upper bound on its book thickness is 5.