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

查看全文 作　　者：LV Da [1]Mei;LIN Wen [2]Song;SONG Zeng [2]Min 高影响力作者 机构地区：[1]Department of Mathematics, Nantong University, Jiangsu 226001, China;[2]Department of Mathematics, Southeast University, Jiangsu 210096, China高影响力机构 出　　处：《Journal of Mathematical Research and Exposition》索引2009年第29卷第1期,共8页高影响力期刊 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). 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 if u and v are at distance two,where |x|m = min{|x|,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. 关 键 词：图论 组合数学 组合学 理论
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