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, II
Journal: Linear Algebra and Its Applications
Volume: 429
Issue: 8-9
First page: 2168
Last page: 2179
Issue Date: 16-Oct-2008
Rank: M22
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.06.018
We continue our investigation of graphs G for which the least eigenvalue λ (G) is minimal among the connected graphs of prescribed order and size. We provide structural details of the bipartite graphs that arise, and study the behaviour of λ (G) as the size increases while the order remains constant. The non-bipartite graphs that arise were investigated in a previous paper [F.K. Bell, D. Cvetković, P. Rowlinson, S.K. Simić, Graphs for which the least eigenvalue is minimal, I, Linear Algebra Appl. (2008), doi: 10.1016/j.laa.2008.02.032]; here we distinguish the cases of bipartite and non-bipartite graphs in terms of size.
Keywords: Bipartite graph | Graph spectrum | Largest eigenvalue | Least eigenvalue
Publisher: Elsevier
Project: EPSRC, Grant EP/D010748/1
Serbian Ministry for Science, Grant 144015G

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