Cycles identifying vertices and edges in binary hypercubes and 2-dimensional tori

Authors:
Iiro Honkala;Mark G. Karpovsky;Simon Litsyn
Affiliations:
Department of Mathematics, University of Turku, 20014 Turku, Finland;College of Engineering, Boston University, Boston, MA;Department of Electrical Engineering - Systems, Tel-Aviv University, Ramat-Aviv 69978, Israel
Venue:
Discrete Applied Mathematics
Year:
2003

Citing 9
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Abstract

A set of subgraphs C1,C2,....,Ck in a graph G is said to identify the vertices (resp. the edges) if the sets {j: v ∈ Cj} (resp. {j: e ∈ Cj}) 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 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 endowed with the Lee metric.