Authors: Bell, Francis
Cvetković, Dragoš
Rowlinson, Peter
Simić, Slobodan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Graphs for which the least eigenvalue is minimal, I
Journal: Linear Algebra and Its Applications
Volume: 429
Issue: 1
First page: 234
Last page: 241
Issue Date: 1-Jul-2008
Rank: M22
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.02.032
Abstract: 
Let G be a connected graph whose least eigenvalue λ(G) is minimal among the connected graphs of prescribed order and size. We show first that either G is complete or λ(G) is a simple eigenvalue. In the latter case, the sign pattern of a corresponding eigenvector determines a partition of the vertex set, and we study the structure of G in terms of this partition. We find that G is either bipartite or the join of two graphs of a simple form.
Keywords: Graph spectrum | Largest eigenvalue | Least eigenvalue | Nested split graph
Publisher: Elsevier
Project: EPSRC, Grant EP/D010748/1
Serbian Ministry for Science, Grant 144015G

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