L(2,1)-labelings of Cartesian Products of Two Cycles


For full text, please see Discrete Applied Mathematics, Volume 154, issue 10, 15 June 2006, Pages 1522-1540

doi: http://dx.doi.org/10.1016/j.dam.2005.12.006


An L(2,1)-labeling of a graph is an assignment of nonnegative integers to its vertices so that adjacent vertices get labels at least two apart and vertices at distance two get distinct labels. The λ-number of a graph G, denoted by λ(G), is the minimum range of labels taken over all of its L(2,1)-labelings. We show that the λ-number of the Cartesian product of any two cycles is 6, 7 or 8. In addition, we provide complete characterizations for the products of two cycles with λ-number exactly equal to each one of these values.


Physical Sciences and Mathematics

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