2026-09-19T12:43:22Zhttps://wakespace.lib.wfu.edu/server/oai/request

oai:null:10339/907592026-09-18T11:50:39Zcom_10339_14934col_10339_38132

Farmer, Charles Matthew 2018-05-24T08:36:19Z 2018-05-24T08:36:19Z 2018 https://wakespace.lib.wfu.edu/handle/10339/90759 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. en Wake Forest University Edge Labelings on the Partially Ordered Set of Non-Crossing Bonds Thesis Hallam, Joshua W Allen, Edward E Howards, Hugh N Mathematics and Statistics open.access