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

  • Authors:
  • Pranava K. Jha

  • Affiliations:
  • Department of Computer Science, St. Cloud State University, 720 Fourth Ave. S., St. Cloud, MN

  • Venue:
  • Information Processing Letters
  • Year:
  • 2003

Quantified Score

Hi-index 0.89

Visualization

Abstract

If r ≥ 1, and m and n are each a multiple of (r + 1)2 + r2, then each isomorphic component of Cm × Cn admits of a vertex partition into (r + 1)2 + r2 perfect r-dominating sets. The result induces a dense packing of Cm × Cn by means of vertexdisjoint subgraphs, each isomorphic to a diagonal array. Areas of applications include efficient resource placement in a diagonal mesh and error-correcting codes.