We consider the L(p,q)-Edge-Labelling problem, which is the edge variant of the well-known L(p,q)-Labelling problem. So far, the complexity of this problem was only partially classified. We complete this study for all nonnegative p and q, by showing that, whenever (p,q) is not (0,0), L(p,q)-Edge-Labelling problem is NP-complete. We do this by proving that for all nonnegative p and q, except p=q=0, there exists an integer k so that L(p,q)-Edge-k-Labelling is NP-complete.

翻译：我们认为L(p,q)-Edge-Labelling问题,这是众所周知的L(p,q)-Labelling问题的边缘变体。到目前为止,这个问题的复杂性只是部分分类。我们通过显示(p,q)没有(0,0,L(p,q)-Edge-Labelling问题是NP-完成的,来证明(p,q)-L(dge,q)-Labelling问题不是完全的。我们证明,除p=q=0外,所有非否定的p和q(q)-q)-L(p,q)-Edge-K-Lalelling问题都存在整数 k,因此L(p,q)-Edge-k-Labelling是全数的。