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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: On multiple eigenvalues of trees
Author(s): Rowlinson, Peter
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Keywords: Graph
Star complement
Issue Date: Jun-2010
Citation: Rowlinson P (2010) On multiple eigenvalues of trees, Linear Algebra and Its Applications, 432 (11), pp. 3007-3011.
Abstract: Let T be a tree of order n>6 with μ as a positive eigenvalue of multiplicity k. Star complements are used to show that (i) if k>n/3 then μ=1, (ii) if μ=1 then, without restriction on k, T has k+1 pendant edges that form an induced matching. The results are used to identify the trees with a non-zero eigenvalue of maximum possible multiplicity.
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Rights: Published in Linear Algebra and its Applications by Elsevier; Elsevier believes that individual authors should be able to distribute their accepted author manuscripts for their personal voluntary needs and interests, e.g. posting to their websites or their institution’s repository, e-mailing to colleagues. The Elsevier Policy is as follows: Authors retain the right to use the accepted author manuscript for personal use, internal institutional use and for permitted scholarly posting provided that these are not for purposes of commercial use or systematic distribution. An "accepted author manuscript" is the author’s version of the manuscript of an article that has been accepted for publication and which may include any author-incorporated changes suggested through the processes of submission processing, peer review, and editor-author communications.

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