On the total restrained domination number of direct products of graphs

Wai Chee Shiu*, Hong-Yu Chen, Xue-Gang Chen, Pak Kiu Sun

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)
20 Downloads (Pure)

Abstract

Let G = (V,E) be a graph. A total restrained dominating set is a set S ⊆ V where every vertex in V \ S is adjacent to a vertex in S as well as to another vertex in V \ S, and every vertex in S is adjacent to another vertex in S. The total restrained domination number of G, denoted by γ t r(G), is the smallest cardinality of a total restrained dominating set of G. We determine lower and upper bounds on the total restrained domination number of the direct product of two graphs. Also, we show that these bounds are sharp by presenting some infinite families of graphs that attain these bounds.

Original languageEnglish
Pages (from-to)629-641
Number of pages13
JournalDiscussiones Mathematicae - Graph Theory
Volume32
Issue number4
DOIs
Publication statusPublished - Dec 2012

Scopus Subject Areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

User-Defined Keywords

  • total domination number
  • total restrained domination number
  • direct product of graphs

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