Quaestiones Mathematicae

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Partitioning the vertices of a graph into two total dominating sets

Pamela Delgado, Wyatt J. Desormeaux, Teresa W. Haynes


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 self-complementary graph with minimum degree at least two has such a partition.

Mathematics Subject Classification (2010): 05C69.

Keywords: Total domination, vertex partitions, dominating sets, self-complementary graphs
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