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.