The Laplacian Spread of a Tree
Yi-Zheng Fan, Jing Xu, Yi Wang, Dong Liang
Abstract
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.
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