Biregular graphs with three eigenvalues

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.

28 pages

Cited by in corpus (10)

• Equiangular lines in Euclidean spaces
• On regular graphs with four distinct eigenvalues
• Graphs with three eigenvalues and second largest eigenvalue at most 1
• On main eigenvalues of certain graphs
• Recent progress on graphs with fixed smallest eigenvalue
• Connected triangle-free planar graphs whose second largest eigenvalue is at most 1
• Characterization of graphs with some normalized Laplacian eigenvalue of multiplicity n-3
• Infinite classes of strongly regular graphs derived from $GL(n,F_2)$
• Graphs with at most three distance eigenvalues different from $-1$ and $-2$
• On graphs with three or four distinct normalized Laplacian eigenvalues