Equitable L(2,1)-labelings of Sierpinski graphs
Hong-Yong Fu, Xie De-zheng · 2010
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 λe(G) ofG is the smallest integer k such that G has an equitable L(2, 1)-labeling. Sierpiński 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 ≥ 2andany k ≥ 2, λe(S(n, k)) = 2k.