Discrete Mathematics & Theoretical Computer Science,Vol 10, No 1 (2008)

摘要

The Laplacian spread of a graph is defined to be the difference between the largest eigenvalueand the second smallest eigenvalue of the Laplacian matrix of the graph.In this paper, we show that the star is the unique tree with maximal Laplacian spread among all trees of given order,and the path is the unique one with minimal Laplacian spread among all trees of given order.