Biregular graphs with three eigenvalues

Dedicated to Misha Klin on the occasion of his retirement
https://doi.org/10.1016/j.ejc.2016.03.004Get rights and content
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Abstract

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.

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