A characterization of L(2, 1)-labeling number for trees with maximum degree 3
Combinatorics
2015-09-02 v1
Abstract
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.
Cite
@article{arxiv.1509.00275,
title = {A characterization of L(2, 1)-labeling number for trees with maximum degree 3},
author = {Dong Chen and Wai Chee Shiu and Qiaojun Shu and Pak Kiu Sun and Weifan Wang},
journal= {arXiv preprint arXiv:1509.00275},
year = {2015}
}