Equitable L(2, 1)-labelings of Sierpinski graphs

An L(2, 1)-labeling of a graph G is equitable if the number of elements in any two color classes differ by at most one. The equitable L(2, 1)-labeling number lambda(e)(G) of G is the smallest integer k such that G has an equitable L(2, 1)-labeling. Sierpinski graphs S(n, k) generalize the Tower of Hanoi graphs- the graph S(n, 3) is isomorphic to the graph of the Tower of Hanoi with n disks. In this paper, we show that for any n >= 2 and any k >= 2, lambda(e)(S(n, k)) = 2k.