Optimal L(2, 1, 1)-Labelings of Caterpillars  

作　　者：Xiaoling ZHANG 

机构地区：[1]Teachers College,Jimei University,Fujian 361021,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2023年第2期150-160,共11页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 11601265);the Scientific Research Foundation of Jimei University (Grant No. Q202201)。

摘　　要：An L(2, 1, 1)-labeling of a graph G is an assignment of non-negative integers(labels) to the vertices of G such that adjacent vertices receive labels with difference at least 2, and vertices at distance 2 or 3 receive distinct labels. The span of such a labeling is the difference between the maximum and minimum labels used, and the minimum span over all L(2, 1, 1)-labelings of G is called the L(2, 1, 1)-labeling number of G, denoted by λ_(2,1,1)(G). In this paper, we investigate the L(2, 1, 1)-labelings of caterpillars. Some useful sufficient conditions for λ_(2,1,1)(T) = △_(2)(T) =maxuv∈E(T)(d(u) + d(v))) are given. Furthermore, we show that the sufficient conditions we provide are also necessary for caterpillars with △_(2)(T) = 6.

关 键 词：channel assignment L(2 1 1)-labeling SPAN CATERPILLAR 

分 类 号：O157.5[理学—数学]