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

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(upsilon)\ greater than or equal to 1 if d(u, v) = 2 and \f (u) - f (v)\ greater than or equal to 2 if d(u, v) = 1. The L(2, 1)-labefing problem is to find the L(2, 1)-labeling number lambda(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. (C) 2004 Elsevier B.V. All fights reserved.