F3-domination problem of graphs

Chan Wei Chang, David Kuo, Sheng Chyang Liaw, Jing Ho Yan

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Given a graph G and a set S⊆ V(G) a vertex v is said to be 3 -dominated by a vertex w in S if either v=w, or v∉ S and there exists a vertex u in V(G)-S such that P:wuv is a path in G. A set S⊆ V(G)is an 3 -dominating set of G if every vertex v is 3 -dominated by a vertex w in S.The 3 -domination number of G, denoted by γ F3(G), is the minimum cardinality of an 3 -dominating set of G. In this paper, we study the 3 -domination of Cartesian product of graphs, and give formulas to compute the 3 -domination number of Pm×Pnand Pm× Cnfor special m,n.

Original languageEnglish
Pages (from-to)400-413
Number of pages14
JournalJournal of Combinatorial Optimization
Volume28
Issue number2
DOIs
StatePublished - Aug 2014

Keywords

  • Cartesian product
  • Cycle
  • Domination
  • Path

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