| 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 | Abstract: | 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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