Published in
Elsevier, Linear Algebra and its Applications, 11(432), p. 3007-3011, 2010
DOI: 10.1016/j.laa.2010.01.003
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On multiple eigenvalues of trees
Journal article published in 2010 by
Peter Rowlinson
This paper is made freely available by the publisher.
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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.