Domination and total domination in complementary prisms

Teresa W. Haynes, Michael A. Henning, Lucas C. Van Der Merwe

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)

Abstract

Let G be a graph and Ḡ be the complement of G. The complementary prism GḠ of G is the graph formed from the disjoint union of G and Ḡ by adding the edges of a perfect matching between the corresponding vertices of G and Ḡ. For example, if G is a 5-cycle, then GḠ is the Petersen graph. In this paper we consider domination and total domination numbers of complementary prisms. For any graph G, max {γ(G), γ(Ḡ)} ≤ γ (Ḡ)and max {γt(G), γt(Ḡ)} ≤ γt (Gγ), where γ(G) and γt(G) denote the domination and total domination numbers of G, respectively. Among other results, we characterize the graphs G attaining these lower bounds.

Original languageEnglish
Pages (from-to)23-37
Number of pages15
JournalJournal of Combinatorial Optimization
Volume18
Issue number1
DOIs
Publication statusPublished - Jul 2009
Externally publishedYes

Keywords

  • Cartesian product
  • Complementary prism
  • Domination
  • Total domination

ASJC Scopus subject areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Domination and total domination in complementary prisms'. Together they form a unique fingerprint.

Cite this