A characterization of graphs with disjoint dominating and total dominating sets

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