THE LAPLACIAN SPECTRAL RADIUS OF TREE WITH FIXED DIAMETER
具有固定直径的树的拉普拉斯谱半径

A caterpillar is a tree in which the removal of all pendant vertices gives a path. This paper consider the Laplacian spectral radius of a Caterpillar with fixed diameter and determine the Caterpillar with the largest Laplacian spectral radius. Furthermore, several properties of Caterpillar are discussed.