Journal
TAIWANESE JOURNAL OF MATHEMATICS
Volume 19, Issue 1, Pages 65-75Publisher
MATHEMATICAL SOC REP CHINA
DOI: 10.11650/tjm.19.2015.4411
Keywords
Laplacian eigenvalues; Trees; Pendant vertex; Diameter; Matching number; Domination number
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Funding
- Specialized Research Fund for the Doctoral Program of Higher Education of China [20124407110002]
- National Natural Science Foundation of China [11071089]
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Let m(T) [0, 2) be the number of Laplacian eigenvalues of a tree T in [0, 2), multiplicities included. We give best possible upper bounds for m(T) [0, 2) using the parameters such as the number of pendant vertices, diameter, matching number, and domination number, and characterize the trees T of order n with m(T) [0, 2) = n - 1, n - 2, and [n/2], respectively, and in particular, show that m(T) [0, 2) = [n/2] if and only if the matching number of T is [n/2].
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