On the Laplacian spectral radius of trees with fixed diameter (Q865423)

The author considers the trees on \(n\) vertices with diameter \(d\), ordered by the largest eigenvalue of the Laplacian matrix, and determines the first \(\left\lfloor\frac d2\right\rfloor+1\) trees in this order. For an analogous result on ordering these trees by the largest eigenvalue of the adjacency matrix, see the paper by the author and \textit{J.-Y. Shao} [Linear Algebra Appl. 413, 131-147 (2006; Zbl 1082.05060)].