## Electronic Theses and Dissertations

#### Degree Name

MS (Master of Science)

#### Program

Mathematical Sciences

8-2021

#### Committee Chair or Co-Chairs

Robert B. Gardner

#### Committee Members

Robert A. Beeler, Rodney Keaton

#### Abstract

Let $M_v$ denotes a complete mixed graph on $v$ vertices, and let $S_6^i$ 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 $\lambda$-fold decomposition of a complete mixed graph into $S_6^i$ for $i\in\{1,2,3,4\}$. We used the difference method for our proof in some cases. We also give some general sufficient conditions for the existence of $S_6^i$-decomposition of the complete bipartite mixed graph for $i\in\{1,2,3,4\}$. Finally, this work introduces the decomposition of a complete mixed graph with a hole into mixed stars.

#### Document Type

Thesis - unrestricted