On the Identification of Vertices and Edges Using Cycles

Authors:
Iiro S. Honkala;Mark G. Karpovsky;Simon Litsyn
Affiliations:
-;-;-
Venue:
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Year:
2001

Citing 11
Cited 1

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On a new class of codes for identifying vertices in graphs

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Sequences of optimal identifying codes

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Two families of optimal identifying codes in binary Hamming spaces

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Watching systems in graphs: An extension of identifying codes

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Abstract

The subgraphs C1, C2, ..., Ck of a graph G are said to identify the vertices (resp. the edges) of G if the sets {j : v 驴 Cj} (resp. {j : e 驴 Cj}) are nonempty for all the vertices v (edges e) and no two are the same. We consider the problem of minimizing k when the subgraphs Ci are required to be cycles or closed walks. The motivation comes from maintaining multiprocessor systems, and we study the cases when G is the binary hypercube, or the two-dimensional p-ary space with respect to the Lee metric.