L(1,1)-Labeling of direct product of cycles

An L(1, 1)-labeling of a graph G is an assignment of labels from {0, 1, ... , k} to the vertices of G such that two vertices that are adjacent or have a common neighbor receive distinct labels. The lambda(1)(1)-number lambda(1)(1) (G) of G is the minimum value k such that G admits an L(1, 1)-labeling. We establish the lambda(1)(1)-numbers for direct product of cycles C-m x C-n for all positive m, n >= 3, where both m, n are even or when one of them is even and the other odd.