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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
Authors: 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
Publisher: Elsevier
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.
Type: Journal Article
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Rights: Made available under an Elsevier Open Archive user license: Articles published under an Elsevier user license are protected by copyright and may be used for non-commercial purposes. Users may access, download, copy, display, redistribute, adapt, translate, text mine and data mine the articles provided that users: •Cite the article using an appropriate bibliographic citation (i.e. author(s), journal, article title, volume, issue, page numbers, DOI and the link to the definitive published version on ScienceDirect) •Use the article for non- commercial purposes •Maintain the integrity of the article •Retain copyright notices and links to these terms and conditions so it is clear to other users what can and cannot be done with the article •Ensure that, for any content in the article that is identified as belonging to a third party, any re-use complies with the copyright policies of that third party This is a non commercial license where the use of published articles for commercial purposes is prohibited.
Affiliation: University of Stirling
University of Belgrade
Mathematics - CSM Dept
Mathematical Institute SANU

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