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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Graphs for which the least eigenvalue is minimal, I
Author(s): Bell, Francis K
Cvetkovic, Dragos
Rowlinson, Peter
Simic, Slobodan K
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Keywords: Graph spectrum
Largest eigenvalue
Least eigenvalue
Nested split graph
Issue Date: Jul-2008
Date Deposited: 28-Jan-2014
Citation: Bell FK, Cvetkovic D, Rowlinson P & Simic SK (2008) Graphs for which the least eigenvalue is minimal, I. Linear Algebra and Its Applications, 429 (1), pp. 234-241.
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.
DOI Link: 10.1016/j.laa.2008.02.032
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