An \(L(2,\, 1)\)-labeling of a graph \(G\) is an assignment of labels from \(\{0,1,\dots,\lambda\}\) to the vertices of \(G\) such that vertices at distance two get different labels and adjacent vertices get labels that are at least two apart. The \(\lambda\)-number of \(G\) is the minimum value \(\lambda\), such that \(G\) admits an \(L(2,\, 1)\)-labeling. The authors generalize the \(L(2,\,1)\)-labeling to the \(L(d_1,d_2,d_3)\)-labeling and establish upper bounds for planar and other graphs.