On L(2,1)-labelings of Cartesian products of paths and cycles Original Research Article

A k-L(2,1)-labeling of a graph G is a function f from the vertex set V(G) to {0,1,…,k} such that |f(u)−f(v)|⩾1 if d(u,v)=2 and |f(u)−f(v)|⩾2 if d(u,v)=1. The L(2,1)-labeling problem is to find the L(2,1)-labeling number λ(G) of a graph G which is the minimum cardinality k such that G has a k-L(2,1)-labeling. In this paper, we study L(2,1)-labeling numbers of Cartesian products of paths and cycles.