An L(2,1)-labeling of a graph G is a function f from the vertex set V(G) to the set of all nonnegative integers such that |f(x)−f(y)|≥2 if d(x,y)=1 and |f(x)−f(y)|≥1 if d(x,y)=2, where d(x,y) denotes the distance between x and y in G. The L(2,1)-labeling number λ(G) of G is the smallest number k such that G has an L(2,1)-labeling with max{f(v):v∈V(G)}=k. Griggs and Yeh conjecture that λ(G)≤Δ2 for any simple graph with maximum degree Δ≥2. This work considers the graph formed by the skew product and the converse skew product of two graphs. As corollaries, the new graph satisfies the above conjecture (with minor exceptions).