Note: On the (h,k)-domination numbers of iterated line digraphs

  • Authors:

  • Toru Hasunuma;Mayu Otani

  • Affiliations:

  • -;-

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2012

Quantified Score

Hi-index 0.04

Visualization

Abstract

An (h,k)-dominating set in a digraph G is a subset D of V(G) such that the subdigraph induced by D is h-connected and for every vertex v of G, v is in-dominated and out-dominated by at least k vertices in D. The (h,k)-domination number @c"h","k(G) of G is the minimum cardinality of an (h,k)-dominating set in G. An (h,k)-dominating set finds applications to fault-tolerant location problems of resources in communication networks and fault-tolerant virtual backbone in wireless networks. Let G be a connected d-regular digraph and 1@?k=2 and 0@?h@?min{k,@?d2@?}. From our results, the (h,k)-domination numbers of d-ary (generalized) de Bruijn and Kautz digraphs are determined for 0@?h@?min{k,@?d2@?}, which strengthen the previously known results on (generalized) de Bruijn and Kautz digraphs.