Biregular graphs with three eigenvalues. (August 2016)

• Record Type: Journal Article
• Authors: Cheng, Xi-Ming; Gavrilyuk, Alexander L.; Greaves, Gary R.W.; Koolen, Jack H.
• Is Part Of: European journal of combinatorics. Volume 56(2016:Aug.)
• Page Start: 57
• Page End: 80
• Publication Date: 2016-08
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2016.03.004
• Languages: English
• ISSNs: 0195-6698

Abstract

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.