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

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.

Grantor dc:publisher

Wake Forest University

Year dc:date.issued

2018

Author dc:creator

• Farmer, Charles Matthew

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10339/90759

OAI identifier oai:identifier

oai:wakespace.lib.wfu.edu:10339/90759