On the Laplacian spectral radius of a tree.
The Laplacian matrix of a graph is the difference of the diagonal matrix of its vertex degrees and its adjacency matrix. The Laplacian spectral radius of a graph is the largest eigenvalue of its Laplacian matrix. This paper gives upper bounds on the Laplacian spectral radius of trees, in terms of the size of a maximum matching in it, and the number of vertices. In several cases, it is shown that the bounds are sharp.
scientific article; zbMATH DE number 1956813