On the largest eigenvalue of a tree with perfect matchings Original Research Article

The set of trees with n vertices and the set of trees with perfect matchings are denoted by Fn and T2k, respectively. M. Hofmeister determined the first five maximum value of the largest eigenvalue of trees in Fn and gave the corresponding trees (Linear Algebra Appl. 260 (1997) 43–59). Focusing on the largest eigenvalue of trees in T2k, this paper will give the first seven maximum value of that of trees in T2k and their corresponding trees. In other words, an order of trees in T2k by their largest eigenvalues is extended to the seventh position.