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Edge Labelings on the Partially Ordered Set of Non-Crossing Bonds

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title
Edge Labelings on the Partially Ordered Set of Non-Crossing Bonds
author
Farmer, Charles Matthew
abstract
Let G be a graph with a finite vertex set and edge set. A bond of G is a spanning subgraph of G whose connected components are induced. This collection of bonds form a partially ordered set which is also a lattice. This lattice has what is known as an ER-labeling. We explore a new subposet of this lattice which we call the “non-crossing bond poset” for all graphs finite graphs. Then we aim to show when this subposet has the desired ER-labeling and when it does not. This paper will focus on what the bond lattice of a graph is, examples of when the non-crossing bond poset has an ER-labeling and when it does not, and the classification of all graphs whose non-crossing bond poset has an ER-labeling. Once such graphs have been found, we then attempt to find the characteristic polynomials of such posets.
contributor
Hallam, Joshua W (committee chair)
Allen, Edward E (committee member)
Howards, Hugh N (committee member)
date
2018-05-24T08:36:19Z (accessioned)
2018-05-24T08:36:19Z (available)
2018 (issued)
degree
Mathematics and Statistics (discipline)
identifier
http://hdl.handle.net/10339/90759 (uri)
language
en (iso)
publisher
Wake Forest University
type
Thesis

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