点接拟梯子的L(2,1,1)-标号

The L(2,1,1)-labelings of the Point-Join-Similarity Ladders

一个图G的L(2,1,1)-标号是指从顶点集V(G)到非负整数集的一个映射f,且使得:当d(u,v)=1时,|f(u)-f(v)|≥2;当d(u,v)=2或3时,|f(u)-f(v)|≥1.不妨假设设最小的标号为0.则,G的L(2,1,1)-标号数λ(G)是G的所有L(2,1,1)-标号下的跨度max{f(v);v∈V(G)}的最小值.完全确定了点接拟梯子的L(2,1,1)-标号数.

An L(2,1,1)-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)|≥2 if d(u,v)=1, and |f(u)-f(v)|≥1 if d(u,v)=2 or 3. Without loss of generality, we let the least label be 0. The L(2,1,1)-labeling number λ(G) of G is the smallest number over the spans max{f(v);v∈V(G)}of all L(2,1,1)-labelings of G. In this paper, we completely determine the L(2,1,1)-labeling number ofthe point-join-similarity ladder.