On L(2,1)-labellings of distance graphs

作     者：陶昉昀 顾国华 许克祥 Tao Fangyun;Gu Guohua;Xu Kexiang

作者机构：南京林业大学信息科学技术学院数学系南京210037 东南大学数学系南京210096 南京航空航天大学理学院南京210016 

出 版 物：《Journal of Southeast University(English Edition)》 (东南大学学报（英文版）)

年 卷 期：2005年第21卷第2期

页      面：244-248页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：TheNationalNaturalScienceFoundationofChina(No. 10171013) 

主　　题：channel assignment problem L(2,1)-labelling distance graphs 

摘      要：The L(2,1)-labelling number of distance graphs G(D), denoted by λ(D), isstudied. It is shown that distance graphs satisfy λ(G) ≤Δ~2. Moreover, we prove λ({1,2, ..., k})=2k +2 and λ({1,3,..., 2k -1}) =2k + 2 for any fixed positive integer k. Suppose k, a ∈ N and k,a≥2. If k≥a, then λ({a, a + 1,..., a + k - 1}) = 2(a + k-1). Otherwise, λ({a, a + 1, ..., a + k- 1}) ≤min{2(a + k-1), 6k -2}. When D consists of two positive integers,6≤λ(D)≤8. For thespecial distance sets D = {k, k + 1}(any k ∈N), the upper bound of λ(D) is improved to 7.