| Affiliation: | (1) Department of Mathematics, Nanjing Normal University, Nanjing, 210097, China;(2) Department of Mathematics, Anhui University, Hefei, 230039, China |
| 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 matchingnumber is 1 or 2,the answer is negative;otherwise,there exists a tree with that matching number which has (hasnot) the eigenvalue 2.In particular,we determine all trees with matching number 3 which has the eigenvalue2. |
