| Title: | Codes and L(2,1)-labelings in Sierpiński graphs |
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| Authors: | ID Gravier, Sylvain (Author)
ID Klavžar, Sandi (Author)
ID Mollard, Michel (Author) |
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| Files: |  http://www.math.nthu.edu.tw/~tjm/myweb/FrameConAbs.htm
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | PEF - Faculty of Education
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| Abstract: | The ▫$lambda$▫-number of a graph ▫$G$▫ is the minimum value ▫$lambda$▫ such that ▫$G$▫ admits a labeling with labels from ▫${0, 1,..., lambda}$▫ 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 graphs - the graph ▫$S(n,3)$▫ is isomorphic to the graph of the Tower of Hanoi with ▫$n$▫ disks. It is proved that for any ▫$n ge $▫2 and any ▫$k ge 3$▫, ▫$lambda (S(n,k)) = 2k$▫. To obtain the result (perfect) codes in Sierpiński graphs are studied in detail. In particular a new proof of their (essential) uniqueness is obtained.
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| Keywords: | matematika, teorija grafov, ▫$L(2,1)$▫-označitev, ▫$lambda$▫-število, grafovske kode, popolne kode, grafi Sierpińskega, mathematics, graph theory, ▫$L(2,1)▫$-labelings, ▫$lambda$▫-number, codes in graphs, perfect codes, Sierpiński graphs |
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| Year of publishing: | 2005 |
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| Number of pages: | str. 671-681 |
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| Numbering: | Vol. 9, no. 4 |
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| PID: | 20.500.12556/DKUM-51513  |
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| UDC: | 519.17 |
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| ISSN on article: | 1027-5487 |
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| COBISS.SI-ID: | 13843801 |
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| NUK URN: | URN:SI:UM:DK:NCRIDAUC |
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| Publication date in DKUM: | 10.07.2015 |
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| Views: | 1490 |
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| Downloads: | 76 |
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| Metadata: |    |
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| Categories: | Misc.
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