Restricted total domination in graphs

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11 Citations (Scopus)

Abstract

The k-restricted total domination number of a graph G is the smallest integer rk(G, γt) such that given any subset U of k vertices of G, there exists a total dominating set of G of cardinality at most rk(G, γt) containing U. Hence, the k-restricted total domination number of a graph G measures how many vertices are necessary to totally dominate a graph if an arbitrary set of k vertices must be included in the total dominating set. When k = 0, the k-restricted total domination number is the total domination number. In this paper we establish upper bound on the k-restricted total domination number of a connected graph in terms of the order and the size of the graph.

Original languageEnglish
Pages (from-to)25-44
Number of pages20
JournalDiscrete Mathematics
Volume289
Issue number1-3
DOIs
Publication statusPublished - 28 Dec 2004
Externally publishedYes

Keywords

  • Bounds
  • Restricted total domination number
  • Total dominating set

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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