3 research outputs found
Partially Oriented 6-star Decomposition of Some Complete Mixed Graphs
Let denotes a complete mixed graph on vertices, and let denotes the partial orientation of the 6-star with twice as many arcs as edges. In this work, we state and prove the necessary and sufficient conditions for the existence of -fold decomposition of a complete mixed graph into for . We used the difference method for our proof in some cases. We also give some general sufficient conditions for the existence of -decomposition of the complete bipartite mixed graph for . Finally, this work introduces the decomposition of a complete mixed graph with a hole into mixed stars