An L(2, 1)-labeling of a graph is an assignment of nonnegative integers to the vertices of G such that adjacent vertices have numbers at least 2 apart, and vertices at distance 2 have distinct numbers.The L(2, 1)-labeling number is the minimum range of labels over all such labeling.It was shown by Griggs and Yeh [Labelling graphs with a condition at distance 2, SIAM J.Discrete Math.5(1992)586-595] that the L(2, 1)-labeling number of a tree is either △ + 1 or △ + 2.