Partitioning the Vertices of a Graph into Two Total Dominating Sets

• Published in: Quaestiones mathematicae Vol. 39; no. 7; pp. 863 - 873
• Main Authors: Delgado, Pamela, Desormeaux, Wyatt J., Haynes, Teresa W.
• Format: Journal Article
• Language: English
• Published: Grahamstown Taylor & Francis 04-11-2016; Taylor & Francis Ltd
• Subjects: dominating sets; self-complementary graphs; Total domination; vertex partitions
• ISSN: 1607-3606; 1727-933X
• DOI: 10.2989/16073606.2016.1188862

A total dominating set in a graph G is a set S of vertices of G such that every vertex in G is adjacent to a vertex of S. We study graphs whose vertex set can be partitioned into two total dominating sets. In particular, we develop several sufficient conditions for a graph to have a vertex partition into two total dominating sets. We also show that with the exception of the cycle on five vertices, every selfcomplementary graph with minimum degree at least two has such a partition.