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arXiv · 1509.00275

A characterization of L(2, 1)-labeling number for trees with maximum degree 3

Dong Chen·Wai Chee Shiu·Qiaojun Shu·Pak Kiu Sun·Weifan Wang
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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.

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Dong Chen, Wai Chee Shiu, Qiaojun Shu, Pak Kiu Sun, Weifan Wang. 2015-09-01. A characterization of L(2, 1)-labeling number for trees with maximum degree 3. https://arxiv.org/abs/1509.00275

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