\(L(p,q)\) labeling of \(d\)-dimensional grids (Q2370453)

\(L(p,q)\) labeling of a graph is a labeling of its vertices by integers from \([0;M]\), in such a way that the values assigned to neighbouring vertices differ by at least \(p\), while vertices at distance 2 obtain values differing by at least \(q\). The minimum value of \(M\) is the \(\lambda\)-number of \(G\) and is denoted by \(\lambda^p_q(G)\). In the paper \(\lambda^p_q(G)\) is studied in the case when \(G\) is a \(d\)-dimensional grid.