  An L(2, 1)-labeling of a graph is an assignment of nonnegative integers to
the vertices of G such that adjacent vertices receive numbers differed by at
least 2, and vertices at distance 2 are assigned 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 \D+ 1 or \D + 2. In this paper, we give a complete
characterization of L(2, 1)-labeling number for trees with maximum degree 3.

Combinatorics