Portland State University. Department of Mathematics and Statistics
Date of Award
Doctor of Philosophy (Ph.D.) in Mathematical Sciences
Mathematics and Statistics
1 online resource (x, 94 pages)
Spanning trees (Graph theory), Trees (Graph theory)
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.
Mahoney, James Raymond, "Tree Graphs and Orthogonal Spanning Tree Decompositions" (2016). Dissertations and Theses. Paper 2944.