Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
8-2020
Committee Chair or Co-Chairs
Bob Gardner
Committee Members
Robert Beeler, Teresa Haynes, Rodney Keaton
Abstract
In the study of mixed graphs, a common question is: What are the necessary and suffcient conditions for the existence of a decomposition of the complete mixed graph into isomorphic copies of a given mixed graph? Since the complete mixed graph has twice as many arcs as edges, then an obvious necessary condition is that the isomorphic copies have twice as many arcs as edges. We will prove necessary and suffcient conditions for the existence of a decomposition of the complete mixed graphs into mixed stars with two edges and four arcs. We also consider some special cases of decompositions of the complete mixed graph into partially oriented stars with twice as many arcs as edges. We employ difference methods in most of our constructions when showing suffciency. 2
Document Type
Thesis - embargo
Recommended Citation
Culver, Chance, "Decompositions of the Complete Mixed Graph by Mixed Stars" (2020). Electronic Theses and Dissertations. Paper 3782. https://dc.etsu.edu/etd/3782
Copyright
Copyright by the authors.