Decompositions of Mixed Graphs with Partial Orientations of the P4.

Meadows, Adam M.

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East Tennessee State University

Decompositions of Mixed Graphs with Partial Orientations of the P4.

dc:creator Meadows, Adam M.

thesis:degree_name MS (Master of Science)

dc:date.issued2009

Abstract

dc:description.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.

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: 2009

Author and committee

dc:creator, dc:contributor.*

Author dc:creator: Meadows, Adam M.

Subjects

dc:subject × 7

Rights

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Statement dc:rights: Copyright by the authors.

Identifiers

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Repository record dc:identifier: https://dc.etsu.edu/etd/1870
OAI identifier oai:identifier: oai:dc.etsu.edu:etd-3222

Decompositions of Mixed Graphs with Partial Orientations of the P<sub>4</sub>.