East Tennessee State University
Restricted and Unrestricted Coverings of Complete Bipartite Graphs with Hexagons
Abstract
dc:description.abstract<p>A minimal covering of a graph G with isomorphic copies of graph H is a set {H<sub>1</sub>, H<sub>2</sub>, H<sub>3</sub>, ... , H<sub>n</sub>} where H<sub>i</sub> is isomorphic to H, the vertex set of H<sub>i</sub> is a subset of G, the edge set of G is a subset of the union of H<sub>i</sub>'s, and the cardinality of the union of H<sub>i</sub>'s minus G is minimum. Some studies have been made of covering the complete graph in which case an added condition of the edge set of H<sub>i</sub> is the subset of the edge set of G for all i which implies no additional restrictions. However, if G is not the complete graph, then this condition may have implications. We will give necessary and sufficient conditions for minimal coverings of complete bipartite graph with 6-cycles, which we call minimal unrestricted coverings. We also give necessary and sufficient conditions for minimal coverings of the complete bipartite graph with 6-cycles with the added condition the edge set of H<sub>i</sub> is a subset of G for all i, and call these minimal restricted coverings.</p>
Degree
thesis:*- Name thesis:degree_name
- MS (Master of Science)
- Level thesis:degree_level
- Thesis - unrestricted
- Discipline thesis:degree_discipline
- Mathematical Sciences
- Year dc:date.issued
- 2013
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Surber, Wesley M
Subjects
dc:subject × 8Rights
dc:rights- Statement dc:rights
-
- Copyright by the authors.
Identifiers
dc:identifier.*- Repository record dc:identifier
- https://dc.etsu.edu/etd/1136
- OAI identifier oai:identifier
- oai:dc.etsu.edu:etd-2315