A characterization of graphs with disjoint dominating and total dominating sets

  • Michael A Henning School of Mathematical Sciences, University of KwaZulu-Natal, Pietermaritzburg, 3209 South Africa
  • Justin Southey School of Mathematical Sciences, University of KwaZulu-Natal, Pietermaritzburg, 3209 South Africa

Abstract

A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a total dominating set of a graph is a set of vertices such that every vertex is adjacent to a vertex in the set. In this paper, we provide a constructive characterization of graphs whose vertex set can be partitioned into a dominating set and a total dominating set.

Keywords: Domination; total domination; vertex partition

Quaestiones Mathematicae 32(2009), 119–129
Published
2009-03-31
Section
Articles

Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606