The minimal Laplacian spectral radius of trees with a given diameter

Abstract

For a graph G , its Laplacian matrix is the difference of the diagonal matrix of its vertex degrees and its adjacency matrix. Let T n , d be the set of trees on n vertices with diameter d . In this paper, for d ∈ { 1 , 2 , 3 , 4 , n − 3 , n − 2 , n − 1 } , trees with minimal Laplacian spectral radii in the set T n , d are characterized.