39th Annual Student Research Conference
Isomorphism Classes of Maximal Chain Descent Orders of the Lattice of Flats of a Graph
Alana M. Ray
Dr. Stephen Lacina, Faculty Mentor
We study the structure of a finite graph G by investigating certain partial orders on the maximal chains in the lattice of flats of G. These partial orders on maximal chains are called maximal chain decent orders (MCDOs), which were introduced by Lacina for any finite, bounded poset that has something called an EL-labeling. Each total order on the edges of G gives rise to an EL-labeling of its lattice of flats, which gives rise to an MCDO. We ask the question: when do different total orders on the edges of G result in isomorphic MCDOs? We give partial answers to this question. When G is a forest or cycle, the MCDOs of G are isomorphic no matter the total order on its edges. When G is two cycles that share an edge, we give an explicit description of the MCDO induced by a total order on its edges.
Keywords: Graphs, Partially Ordered Set, Graph Theory, Lattice of Flats
Topic(s):Mathematics
Presentation Type: Oral Presentation
Session: -2
Location: MG 1000
Time: 8:45