Optimal L(2,1)-labeling of strong products of cycles

The L(2, 1)-labeling of a graph is an abstraction of assigning integer freq uencies to radio transmitters such that i) transmitters that are one unit o f distance apart receive frequencies that differ by at least two, and ii) t ransmitters that are two units of distance apart receive frequencies that d iffer by at least one. The least span of frequencies in such a labeling is referred to as the X-number of the graph. It is shown that if k greater tha n or equal to 1 and m(0),..., m(k-1) are each a multiple of 3(k) + 2, then lambda (Cm-0 boxed times ... boxed times Cmk-1) is equal to the theoretical minimum of 3(k) + 1, where C-i denotes the cycle of length i and boxed tim es denotes the strong product of graphs.