Biregular graphs with three eigenvalues
  We consider nonregular graphs having precisely three distinct eigenvalues. The focus is mainly on the case of graphs having two distinct valencies and our results include constructions of new examples, structure theorems, valency constraints, and a classification of certain special families of such graphs. We also present a new example of a graph with three valencies and three eigenvalues of which there are currently only finitely many known examples. 
Xi-Ming Cheng, Alexander L. Gavrilyuk, Gary R. W. Greaves, Jack H.   Koolen
math.CO