A note on weakly connected domination number in graphs

Xue Gang Chen*, Wai Chee SHIU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Let G be a connected graph. A weakly connected dominating set of G is a dominating set D such that the edges not incident to any vertex in D do not separate the graph G. In this paper, we first consider the relationship between weakly connected domination number γω(G) and the irredundance number ir(G). We prove that γω(G) ≤ 5/2ir(G)-2 and this bound is sharp. Furthermore, for a tree T, we give a sufficient and necessary condition for γc(T) = γω(T) + k, where γc(G) is the connected domination number and 0 ≤ k ≤ γω(T) -1.

Original languageEnglish
Pages (from-to)193-201
Number of pages9
JournalArs Combinatoria
Volume97
Publication statusPublished - Oct 2010

Scopus Subject Areas

  • Mathematics(all)

User-Defined Keywords

  • Connected domination number
  • Domination number
  • Irredundance number
  • Weakly connected domination number

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