L(2,1)-labelings of Cartesian Products of Two Cycles
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
Troxell, Denise and Schwarz, Christopher, "L(2,1)-labelings of Cartesian Products of Two Cycles" (2005). Board of Research Working Papers. 5.