Perfect r-domination in the Kronecker product of three cycles

Author

Jha, Pranava K.

Author_Institution

Dept. of Comput. Sci., St. Cloud State Univ., MN, USA

Volume

49

Issue

1

fYear

2002

fDate

1/1/2002 12:00:00 AM

Firstpage

89

Lastpage

92

Abstract

If r⩾1, and m₀, m₁, and m₂ are each a multiple of (r+1)³+r³, then each isomorphic component of the graph C(m₀)×C(m₁)×C(m₂) permits a vertex partition into (r+1)³+r³ perfect r-dominating sets. The result induces a dense packing of C(m₀)×C(m₁)×C(m₂) by means of vertex-disjoint subgraphs, each isomorphic to a connected component of P_2r+1×P_2r+1×P_2r+1. Additional results include a general lower bound on r-domination number of a Kronecker product of finitely many cycles. Areas of applications include efficient resource placement in communication networks and error-correcting codes

Keywords

error correction codes; graph theory; resource allocation; telecommunication network routing; Kronecker product; communication networks; error-correcting codes; graph theory; isomorphic graph component; network topologies; perfect r-dominating sets; perfect r-domination; r-domination number; resource placement; vertex partition; vertex-disjoint subgraphs; Bipartite graph; Circuits; Tensile stress;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.974881

Filename

974881