Perfect r-domination in the Kronecker product of three cycles
Pranava K. Jha · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · 2002
If r/spl ges/1, and m/sub 0/, m/sub 1/, and m/sub 2/ are each a multiple of (r+1)/sup 3/+r/sup 3/, then each isomorphic component of the graph C(m/sub 0/)/spl times/C(m/sub 1/)/spl times/C(m/sub 2/) permits a vertex partition into (r+1)/sup 3/+r/sup 3/ perfect r-dominating sets. The result induces a dense packing of C(m/sub 0/)/spl times/C(m/sub 1/)/spl times/C(m/sub 2/) by means of vertex-disjoint subgraphs, each isomorphic to a connected component of P/sub 2r+1//spl times/P/sub 2r+1//spl times/P/sub 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.