A characterization of graphs with disjoint total dominating sets

Michael A. Henning, Iztok Peterin

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

A set S of vertices in a graph G is a total dominating set of G if every vertex is adjacent to a vertex in S. A fundamental problem in total domination theory in graphs is to determine which graphs have two disjoint total dominating sets. In this paper, we solve this problem by providing a constructive characterization of the graphs that have two disjoint total dominating sets. Our characterization gives an entirely new description of graphs with two disjoint total dominating sets and places them in another context, developing them from four base graphs and applies a sequence of operations from seventeen operations that are independent and necessary to produce all such graphs. We show that every graph with two disjoint total dominating sets can be constructed using this method.

Original languageEnglish
Pages (from-to)359-375
Number of pages17
JournalArs Mathematica Contemporanea
Volume16
Issue number2
DOIs
Publication statusPublished - 2019

Keywords

  • Disjoint total dominating sets
  • Total domination number

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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