L(j, k)-labeling number of Cartesian 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 |f(u)−f(v)|≥j if d(u,v)=1, and |f(u)−f(v)|≥k if d(u,v)=2. The span of f is the difference between the maximum and the minimum numbers assigned by f. The L(j,k)-labeling number of G, denoted by λj,k(G), is the minimum span over all L(j,k)-labelings of G. In this article, we completely determine the L(j,k)-labeling number (2j≤k) of the Cartesian product of path and cycle.