L（2, 1）-Circular Labelings of Cartesian Products of Complete Graphs

作     者：LV Da Mei LIN Wen Song SONG Zeng Min 

作者机构：Department of Mathematics Nantong University Jiangsu 226001 China Department of Mathematics Southeast University Jiangsu 210096 China 

出 版 物：《Journal of Mathematical Research and Exposition》 (数学研究与评论（英文版）)

年 卷 期：2009年第29卷第1期

页      面：91-98页

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

基　　金：Foundation item: the National Natural Science Foundation of China (No. 10671033) the Science Foundation of Southeast University (No. XJ0607230) the Natural Science Foundation of Nantong University (No. 08Z003) 

主　　题：λ2,1-number σ2,1-number Cartesian product. 

摘      要：For positive integers j and k with j ≥ k, an L（j, k）-labeling of a graph G is an assignment of nonnegative integers to V（G） such that the difference between labels of adjacent vertices is at least j, and the difference between labels of vertices that are distance two apart is at least k. The span of an L（j, k）-labeling of a graph G is the difference between the maximum and minimum integers it uses. The λj, k-number of G is the minimum span taken over all L（j, k）-labelings of G. An m-（j, k）-circular labeling of a graph G is a function f ： V（G） →{0, 1, 2,..., m - 1} such that ｜f（u） - f（v）｜m ≥ j if u and v are adjacent; and ｜f（u） - f（v）｜m 〉 k ifu and v are at distance two, where ｜x｜m = min{｜xl｜, m-｜x｜}. The minimum integer m such that there exists an m-（j, k）-circular labeling of G is called the σj,k-number of G and is denoted by σj,k（G）. This paper determines the σ2,1-number of the Cartesian product of any three complete graphs.