Biregular graphs with three eigenvalues

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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)57-80
Number of pages24
JournalEuropean Journal of Combinatorics
Volume56
DOIs
Publication statusPublished - 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