The L(d,1)-number of powers of paths

AbstractGiven a graph G=(V,E) and a positive integer d, an L(d,1)-labelling of G is a function f:V→{0,1,…} such that if two vertices x and y are adjacent, then |f(x)−f(y)|≥d; if they are at distance 2, then |f(x)−f(y)|≥1. The L(d,1)-number of G, denoted by λd,1(G), is the smallest number m such that G has an L(d,1)-labelling with m=max{f(x)∣x∈V}. We correct the result on the L(d,1)-number of powers of paths given by Chang et al. in [G.J. Chang, W.-T. Ke, D. Kuo, D.D.-F. Liu, R.K. Yeh, On L(d,1)-labelings of graphs, Discrete Math. 220 (2000) 57–66]