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Covering codes in Sierpinski graphs

Laurent Beaudou 1 Sylvain Gravier 2, 3 Sandi Klavžar 4, 5, 6 Matjaz Kovse 2, 6 Michel Mollard 2
1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 IF - Institut Fourier
3 Leibniz - IMAG - Laboratoire Leibniz
4 FMF - Faculty of Mathematics and Physics [Ljubljana]
5 Faculty of Natural Sciences and Mathematics [Maribor]
6 Institute of Mathematics, Physics and Mechanics [Ljubljana]
Abstract : For a graph G and integers a and b, an (a, b)-code of G is a set C of vertices such that any vertex from C has exactly a neighbors in C and any vertex not in C has exactly b neighbors in C. In this paper we classify integers a and b for which there exist (a, b)-codes in Sierpinski graphs.
Mots-clés : codes in graphs perfect codes Sierpinski graphs
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https://hal.inria.fr/hal-00990423
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Laurent Beaudou, Sylvain Gravier, Sandi Klavžar, Matjaz Kovse, Michel Mollard. Covering codes in Sierpinski graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, 12 (3), pp.63-74. ⟨hal-00990423⟩

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