The Laplacian spread of a tree

Yi-Zheng Fan (1, 2) , Jing Xu (1, 2) , Yi Wang (1, 2) , Dong Liang (1)

1 Key Laboratory of Intelligent Computing & Signal Processing [China]
2 School of Mathematical Sciences [Anhui]

The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and 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.

Domaines: Mathématique discrète [cs.DM]

Yi-Zheng Fan, Jing Xu, Yi Wang, Dong Liang. The Laplacian spread of a tree. Discrete Mathematics and Theoretical Computer Science, 2008, Vol. 10 no. 1 (1), pp.79--86. ⟨10.46298/dmtcs.439⟩. ⟨hal-00972305⟩