Defense Date
4-1-2016
Graduation Date
Spring 2016
Availability
Immediate Access
Submission Type
thesis
Degree Name
MS
Department
Computational Mathematics
School
McAnulty College and Graduate School of Liberal Arts
Committee Chair
Karl Wimmer
Committee Member
Rachael Neilan
Committee Member
John Kern
Keywords
Computational, Expansion, Graceful Labeling, Graph Theory, Tree
Abstract
The graceful tree conjecture was first introduced over 50 years ago, and to this day it remains largely unresolved. Ideas for how to label arbitrary trees have been sparse, and so most work in this area focuses on demonstrating that particular classes of trees are graceful. In my research, I continue this effort and establish the gracefulness of some new tree types using previously developed techniques for constructing graceful trees. Meanwhile, little work has been done on developing computational methods for obtaining graceful labelings, as direct approaches are computationally infeasible for even moderately large trees. With this in mind, I have designed a new computational approach for constructing a graceful labeling for trees with sufficiently many leaves. This approach leverages information about the local structures present in a given tree in order to construct a suitable labeling. It has been shown to work for many small cases and thoughts on how to extend this approach for larger trees are put forth.
Format
Language
English
Recommended Citation
Guyer, M. (2016). Common Techniques in Graceful Tree Labeling with a New Computational Approach (Master's thesis, Duquesne University). Retrieved from https://dsc.duq.edu/etd/609