Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
5-2009
Committee Chair or Co-Chairs
Robert A. Beeler
Committee Members
Robert B. Gardner, Teresa W. haynes
Abstract
A decomposition D of a graph H by a graph G is a partition of the edge set of H such that the subgraph induced by the edges in each part of the partition is isomorphic to G. A mixed graph on V vertices is an ordered pair (V,C), where V is a set of vertices, |V| = v, and C is a set of ordered and unordered pairs, denoted (x, y) and [x, y] respectively, of elements of V [8]. An ordered pair (x, y) ∈ C is called an arc of (V,C) and an unordered pair [x, y] ∈ C is called an edge of graph (V,C). A path on n vertices is denoted as Pn. A partial orientation on G is obtained by replacing each edge [x, y] ∈ E(G) with either (x, y), (y, x), or [x, y] in such a way that there are twice as many arcs as edges. The complete mixed graph on v vertices, denoted Mv, is the mixed graph (V,C) where for every pair of distinct vertices v1, v2 ∈ V , we have {(v1, v2), (v2, v1), [v1, v2]} ⊂ C. The goal of this thesis is to establish necessary and sufficient conditions for decomposition of Mv by all possible partial orientations of P4.
Document Type
Thesis - unrestricted
Recommended Citation
Meadows, Adam M., "Decompositions of Mixed Graphs with Partial Orientations of the P4." (2009). Electronic Theses and Dissertations. Paper 1870. https://dc.etsu.edu/etd/1870
Copyright
Copyright by the authors.