CODES AND $L(2,1)$-LABELINGS IN SIERPI\'NSKI GRAPHS
Sylvain Gravier · University of Maribor digital library (University of Maribor) · 2005
Abstract. The -number of a graph G is the minimum value such that G admits a labeling with labels from {0, 1,..., } where vertices at distance two get different labels and adjacent vertices get labels that are at least two apart. Sierpiński graphs S(n, k) generalize the Tower of Hanoi graphsthe graph S(n, 3) is isomorphic to the graph of the Tower of Hanoi with n disks. It is proved that for any n 2 and any k 3, (S(n, k)) = 2k. To obtain the result (perfect) codes in Sierpiński graphs are studied in detail. In particular a new proof of their (essential) uniqueness is obtained. 1.