The L(3, 2, 1)-Labeling Problem for Trees
Received:July 29, 2019  Revised:February 15, 2020
Key Word: channel assignment   L(3, 2, 1)-labeling   trees   diamater  
Fund ProjectL:The National Natural Science Foundation of China (Grant No. 11601265) and High-level Talent Innovation and Entrepreneurship Project of Quanzhou City, China (Grant No. 2017Z033)
Author NameAffiliationE-mail
Xiaoling Zhang Quanzhou Normal University xml000999@163.com 
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Abstract:
      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)j|≥ 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.
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