L(j, k)-number of direct product of path and cycle

For positive numbers j and k, an L(j, k)-labeling f of G is an assignment of numbers to vertices of G such that {pipe}f(u) - f(v){pipe} ≥ j if uv ∈ E(G), and {pipe}f(u) - f(v){pipe} ≥ k if d(u, v) = 2. Then the span of f is the difference between the maximum and the minimum numbers assigned by f. The L(j, k)-number of G, denoted by λ_j,k(G), is the minimum span over all L(j, k)-labelings of G. In this paper, we give some results about the L(j, k)-number of the direct product of a path and a cycle for j ≤ k.