On the Eigenvalue Two and Matching Number of a Tree

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Abstract

In [6], Guo and Tan have shown that 2 is a Laplacian eigenvalue of any tree with perfect matchings. For trees without perfect matchings, we study whether 2 is one of its Laplacian eigenvalues. If the matching number is 1 or 2, the answer is negative; otherwise, there exists a tree with that matching number which has (has not) the eigenvalue 2. In particular, we determine all trees with matching number 3 which has the eigenvalue 2.

Keywords

Tree Laplacian eigenvalues matching number 

2000 MR Subject Classification

05C50 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsNanjing Normal UniversityNanjingChina
  2. 2.Department of MathematicsAnhui UniversityHefeiChina

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