Labelling planar graphs without 4-cycles with a condition on distance two

Let p and q be positive integers. An L(p,q)-labelling of a graph G is a function @f:V(G)->N such that |@f(x)[email protected](y)|>=p if x and y are adjacent and |@f(x)[email protected](y)|>=q if x and y are of distance two apart. The L(p,q)-labelling number @l(G;p,q) of G is the least k for which G has an L(p,q)-labelling @f:V(G)->{0,1,...,k}. In this paper we prove that for every planar graph G without 4-cycles and of maximum degree @D,@l(G;p,q)=

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