Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
8-2014
Committee Chair or Co-Chairs
Teresa Haynes
Committee Members
Robert Gardner, Debra Knisley
Abstract
For a graph G = (V,E), we consider a bipartition {V1,V2} of the vertex set V by placing constraints on the vertices as follows. For every vertex v in Vi, we place a constraint on the number of neighbors v has in Vi and a constraint on the number of neighbors it has in V3-i. Using three values, namely 0 (no neighbors are allowed), 1 (at least one neighbor is required), and X (any number of neighbors are allowed) for each of the four constraints, results in 27 distinct types of bipartitions. The goal is to characterize graphs having each of these 27 types. We give characterizations for 21 out of the 27. Three other characterizations appear in the literature. The remaining three prove to be quite difficult. For these, we develop properties and give characterization of special families.
Document Type
Thesis - unrestricted
Recommended Citation
Delgado, Pamela I., "Bipartitions Based on Degree Constraints" (2014). Electronic Theses and Dissertations. Paper 2410. https://dc.etsu.edu/etd/2410
Copyright
Copyright by the authors.