Optimal L(2, 1)-labeling of strong products of cycles [transmitter frequency assignment]
Pranava K. Jha · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · 2001
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 /spl lambda/-number of the graph. It is shown that if k/spl ges/1 and m/sub 0/, ..., m/sub k-1/ are each a multiple of 3/sup k/+2, then /spl lambda/(Cm/sub 0//spl square/.../spl square/Cm/sub k-1/) is equal to the theoretical minimum of 3/sup k/+1, where C/sub i/ denotes the cycle of length i and /spl square/ denotes the strong product of graphs.