The L（3, 2, 1）-Labeling Problem for Trees

摘要

An L（3,2,1）-labeling of a graph G is a function f from the vertex set V（G） to the set of all non-negative integers（labels） such that |f（u）-f（v）|≥3 if d（u,v）=1,|f（u）-f（v）≥2 if d（u,v）=2 and |f（u）-f（v）|≥1 if d（u,v）=3.For a non-negative integer k,a k-L（3,2,1）-labeling is an L（3,2,1）-labeling such that no label is greater than k.The L（3,2,1）-labeling number of G,denoted by λ3,2,1（G）, is the smallest number k such that G has a k-L（3,2,1）-labeling.In this article,we characterize the L（3,2,1）-labeling numbers of trees with diameter at most 6.