Sponsor
Portland State University. Department of Mathematics and Statistics
First Advisor
John Caughman
Date of Publication
Spring 5-17-2016
Document Type
Dissertation
Degree Name
Doctor of Philosophy (Ph.D.) in Mathematical Sciences
Department
Mathematics and Statistics
Language
English
Subjects
Spanning trees (Graph theory), Trees (Graph theory)
DOI
10.15760/etd.2939
Physical Description
1 online resource (x, 94 pages)
Abstract
Given a graph G, we construct T(G), called the tree graph of G. The vertices of T(G) are the spanning trees of G, with edges between vertices when their respective spanning trees differ only by a single edge. In this paper we detail many new results concerning tree graphs, involving topics such as clique decomposition, planarity, and automorphism groups. We also investigate and present a number of new results on orthogonal tree decompositions of complete graphs.
Rights
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Persistent Identifier
http://archives.pdx.edu/ds/psu/17521
Recommended Citation
Mahoney, James Raymond, "Tree Graphs and Orthogonal Spanning Tree Decompositions" (2016). Dissertations and Theses. Paper 2944.
https://doi.org/10.15760/etd.2939