Advisor

John Caughman

Date of Award

Spring 5-17-2016

Document Type

Dissertation

Degree Name

Doctor of Philosophy (Ph.D.) in Mathematical Sciences

Department

Mathematics and Statistics

Physical Description

1 online resource (x, 94 pages)

Subjects

Spanning trees (Graph theory), Trees (Graph theory)

DOI

10.15760/etd.2939

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.

Persistent Identifier

http://archives.pdx.edu/ds/psu/17521

Included in

Mathematics Commons

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