Authors: Pu Zhang Wensong Lin
Publish Date: 2012/09/18
Volume: 27, Issue: 4, Pages: 695-710
Abstract
Let njk be nonnegative integers An nfold Ljklabeling of a graph G is an assignment f of sets of nonnegative integers of order n to the vertices of G such that for any two vertices uv and any two integers a∈fu b∈fv a−b≥j if uv∈EG and a−b≥k if u and v are distance two apart The span of f is the absolute difference between the maximum and minimum integers used by f The nfold Ljklabeling number of G is the minimum span over all nfold Ljklabelings of GLet njk and m be nonnegative integers An nfold circular mLjklabeling of a graph G is an assignment f of subsets of 01…m−1 of order n to the vertices of G such that for any two vertices uv and any two integers a∈fu b∈fv mina−bm−a−b≥j if uv∈EG and mina−bm−a−b≥k if u and v are distance two apart The minimum m such that G has an nfold circular mLjklabeling is called the nfold circular Ljklabeling number of GThis paper provides upper and lower bounds for the nfold Lj1labeling number and the nfold circular Lj1labeling number of the triangular lattice and determines the nfold L21labeling number and nfold circular L21labeling number of the triangular lattice for n≥3
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