Biregular graphs with three eigenvalues

Xi Ming Cheng; Alexander L. Gavrilyuk; Gary R.W. Greaves; Jack H. Koolen

doi:10.1016/j.ejc.2016.03.004

Biregular graphs with three eigenvalues

Xi Ming Cheng, Alexander L. Gavrilyuk, Gary R.W. Greaves, Jack H. Koolen

INF - Computer and Mathematical Sciences

Research output: Contribution to journal › Article

16 Citations (Scopus)

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.

Original language	English
Pages (from-to)	57-80
Number of pages	24
Journal	European Journal of Combinatorics
Volume	56
DOIs	https://doi.org/10.1016/j.ejc.2016.03.004
Publication status	Published - 2016 Aug 1

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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Cheng, X. M., Gavrilyuk, A. L., Greaves, G. R. W., & Koolen, J. H. (2016). Biregular graphs with three eigenvalues. European Journal of Combinatorics, 56, 57-80. https://doi.org/10.1016/j.ejc.2016.03.004

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