A1 Refereed original research article in a scientific journal
Cycles identifying vertices and edges in binary hypercubes and 2-dimensional tori
Authors: Honkala I, Karpovsky MG, Litsyn S
Publisher: ELSEVIER SCIENCE BV
Publication year: 2003
Journal: Discrete Applied Mathematics
Journal name in source: DISCRETE APPLIED MATHEMATICS
Journal acronym: DISCRETE APPL MATH
Volume: 129
Issue: 2-3
First page : 409
Last page: 419
Number of pages: 11
ISSN: 0166-218X
DOI: https://doi.org/10.1016/S0166-218X(02)00579-6
Abstract
A set of subgraphs C(1), C(2),...,C(k) in a graph G is said to identify the vertices (resp. the edges) if the sets {j: v is an element of C(j)} (resp. {j: e is an element of C(j)}) are nonempty for all the vertices v (edges e) and no two are the same set. We consider the problem of minimizing k when the subgraphs C(i) 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 endowed with the Lee metric. (C) 2003 Elsevier B.V. All rights reserved.
A set of subgraphs C(1), C(2),...,C(k) in a graph G is said to identify the vertices (resp. the edges) if the sets {j: v is an element of C(j)} (resp. {j: e is an element of C(j)}) are nonempty for all the vertices v (edges e) and no two are the same set. We consider the problem of minimizing k when the subgraphs C(i) 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 endowed with the Lee metric. (C) 2003 Elsevier B.V. All rights reserved.
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