Title :
Perfect r-domination in the Kronecker product of three cycles
Author_Institution :
Dept. of Comput. Sci., St. Cloud State Univ., MN, USA
fDate :
1/1/2002 12:00:00 AM
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 P2r+1×P2r+1×P2r+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;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
