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

The L(2, 1)-labeling of a graph is an abstraction of assigning integer frequencies to radio transmitters such that i) transmitters that are one unit of distance apart receive frequencies that differ by at least two, and ii) transmitters that are two units of distance apart receive frequencies that differ 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 than 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 times denotes the strong product of graphs.