Characterizing r-perfect codes in direct products of two and three cycles

Authors:
Janja Jerebic;Sandi Klavžar;Simon Špacapan
Affiliations:
Department of Mathematics and Computer Science, PEF, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia;Department of Mathematics and Computer Science, PEF, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia;University of Maribor, FME, Smetanova 17, 2000 Maribor, Slovenia
Venue:
Information Processing Letters
Year:
2005

Citing 7
Cited 1

Kronecker products of paths and cycles: decomposition, factorization and bi-pancyclicity

Discrete Mathematics - Special issue on Graph theory
Factoring cardinal product graphs in polynomial time

Proceedings of the conference on Discrete metric spaces
Error-correcting codes on the towers of Hanoi graphs

Discrete Mathematics
Processor Scheduling and Allocation for 3D Torus Multicomputer Systems

IEEE Transactions on Parallel and Distributed Systems
Efficient Resource Placement in Hypercubes Using Multiple-Adjacency Codes

IEEE Transactions on Computers
Diagonal and Toroidal Mesh Networks

IEEE Transactions on Computers
Perfect r-domination in the Kronecker product of two cycles, with an application to diagonal/toroidal mesh

Information Processing Letters

Reflections about a single checksum

WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields

Quantified Score

Hi-index	0.89

Visualization

Abstract

An r-perfect code of a graph G=(V,E) is a set C@?V such that the r-balls centered at vertices of C form a partition of V. It is proved that the direct product of C"m and C"n (r=1, m,n=2r+1) contains an r-perfect code if and only if m and n are each a multiple of (r+1)^2+r^2 and that the direct product of C"m, C"n, and C"@? (r=1, m,n,@?=2r+1) contains an r-perfect code if and only if m, n, and @? are each a multiple of r^3+(r+1)^3. The corresponding r-codes are essentially unique. Also, r-perfect codes in C"2"rxC"n (r=2, n=2r) are characterized.