K-Tuple total domination in cross products of graphs

Michael A. Henning, Adel P. Kazemi

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

For k ≥ 1 an integer, a set S of vertices in a graph G with minimum degree at least k is a k-tuple total dominating set of G if every vertex of G is adjacent to at least k vertices in S. The minimum cardinality of a k-tuple total dominating set ofGis the k-tuple total domination number of G. When k = 1, the k-tuple total domination number is the well-studied total domination number. In this paper, we establish upper and lower bounds on the k-tuple total domination number of the cross product graph G×H for any two graphs G and H with minimum degree at least k. In particular, we determine the exact value of the k-tuple total domination number of the cross product of two complete graphs.

Original languageEnglish
Pages (from-to)339-346
Number of pages8
JournalJournal of Combinatorial Optimization
Volume24
Issue number3
DOIs
Publication statusPublished - Oct 2012

Keywords

  • Cross product
  • K-tuple total 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 'K-Tuple total domination in cross products of graphs'. Together they form a unique fingerprint.

Cite this