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The L(2,1)-labeling of a graph is an abstraction of the problem of assigning (integer) frequencies to radio transmitters, such that transmitters that are "close", receive different frequencies, and those that are "very close" receive frequencies that are further apart. The least span of frequencies in such a labeling is referred to as the λ-number of the graph. Let n be odd ≥5, k=(n-3)/2 and let m0,...,mk-1, mk each be a multiple of n. It is shown that λ(Cm0□···□Cmk-1) is equal to the theoretical minimum of n-1, where Cr denotes a cycle of length r and "□" denotes the Cartesian product of graphs. The scheme works for a vertex partition of Cm0□···□Cmk-1□Cmk into smallest (independent) dominating sets.
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on (Volume:47 , Issue: 10 )
Date of Publication: Oct 2000