1-perfect codes in Sierpiński graphs
Sandi Klavžar, Uroš Milutinović, Ciril Petr
Source record
Source: Crossref
Published: Dec 1, 2002
DOI: 10.1017/s0004972700040235
Open original source ↗Source abstract
Sierpiński graphs S ( n , κ) generalise the Tower of Hanoi graphs—the graph S ( n , 3) is isomorphic to the graph H n of the Tower of Hanoi with n disks. A 1-perfect code (or an efficient dominating set) in a graph G is a vertex subset of G with the property that the closed neighbourhoods of its elements form a partition of V ( G ). It is proved that the graphs S ( n , κ) possess unique 1-perfect codes, thus extending a previously known result for H n . An efficient decoding algorithm is also presented. The present approach, in particular the proposed (de)coding, is intrinsically different from the approach to H n .
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.