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
Information Processing Letters
| Hi-index | 0.89 |
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 Cm and Cn (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 + r2 and that the direct product of Cm, Cn, and Cl (r ≥ 1, m, n, l ≥ 2r + 1) contains an r-perfect code if and only if m, n, and l are each a multiple of r3 + (r + 1)3. The corresponding r-codes are essentially unique. Also, r-perfect codes in C2r × Cn (r ≥ 2, n ≥ 2r) are characterized.