点接拟梯子的L(d,1,1)-标号

The L(d,1,1)-labelings of the point-join-similarity ladders

图G的L(d,1,1)-标号指的是顶点集V(G)到非负整数集的一个映射f,且当d(u,v)=1时,|f(u)-f(v)|≥d;当d(u,v)=2时,|f(u)-f(v)|≥1;当d(u,v)=3时,|f(u)-f(v)|≥1。不妨假设最小的标号为0.G的L(d,1,1)-标号数λ(G)指的是G的全部L(d,1,1)-标号下的跨度max{f(v);v∈V(G)}最小值。基本上确定了点接拟梯子的L(d,1,1)-标号数。

An L(d, 1, 1)-labeling of a graph G is a function f from the vertex set V(G) to the set of all nonnegative integers such that |f(u)-f(v)| ≥d if d(u, v) =1,and |f(u)-f(v)| ≥1 if d(u, v) =2 or 3. Without loss of generality,let the least label be 0.The L(d, 1, 1)-labeling number λ(G) of G is the smallest number over the spans max{ f(v);v∈V(G)} of all L(d, 1, 1)-labelings of G.The L(d, 1, 1)-labeling number of the point-join-similarity ladders were almostly determined.