Domination graphs of regular tournaments Original Research Article

Let ℘∗(m,n) denote the set of all graphs that are the union of m even paths and n nontrivial odd paths, and ℘(m,n) denote the set of all graphs that are the union of m even paths and n odd paths. In this paper, we show that if G is the domination graph of a regular tournament then G∈℘(m,n) or G is an odd cycle. Also we give a necessary and sufficient condition for G∈℘∗(m,n) to be the domination graph of a regular tournament. Constructions used in this paper will provide insight into the structure of a large class of regular tournaments.