1-perfect codes in Sierpiński graphs
2002 ◽
Vol 66
(3)
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pp. 369-384
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Keyword(s):
Sierpiński graphs S (n, κ) generalise the Tower of Hanoi graphs—the graph S (n, 3) is isomorphic to the graph Hn 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 Hn. An efficient decoding algorithm is also presented. The present approach, in particular the proposed (de)coding, is intrinsically different from the approach to Hn.
2015 ◽
Vol 120
(22)
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pp. 13-17
2013 ◽
Vol 7
(1)
◽
pp. 72-82
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Keyword(s):
2005 ◽
Vol E88-A
(5)
◽
pp. 1384-1387
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Keyword(s):