## Lattice Structures in Finite Graph Topologies

 dc.contributor.advisor Hart, James en_US dc.contributor.author Frazier, Brian Phillip en_US dc.contributor.committeemember Ye, Dong en_US dc.contributor.committeemember Stephens, Chris en_US dc.contributor.committeemember Seo, Suk en_US dc.contributor.department Basic & Applied Sciences en_US dc.date.accessioned 2015-06-12T19:04:12Z dc.date.available 2015-06-12T19:04:12Z dc.date.issued 2015-08-15 en_US dc.description.abstract In his 2005 dissertation, Antoine Vella studied the relationships between hypergraphs en_US dc.description.abstract and a topological space defined using graph-theoretical concepts called the classical en_US dc.description.abstract topology. In this paper, we take this process a step further to open set lattices en_US dc.description.abstract constructed from these topological spaces. In this paper, we will characterize the en_US dc.description.abstract structure of these lattices entirely for finite simple graphs. We then use these results en_US dc.description.abstract to conjecture on a possible relationship between hypergraphs and open set lattices. en_US dc.description.degree M.S. en_US dc.identifier.uri http://jewlscholar.mtsu.edu/handle/mtsu/4461 dc.publisher Middle Tennessee State University en_US dc.subject Boolean Lattices en_US dc.subject Graph Theory en_US dc.subject Graph Topology en_US dc.subject Lattice Theory en_US dc.subject Order Theory en_US dc.subject Topology en_US dc.subject.umi Mathematics en_US dc.thesis.degreegrantor Middle Tennessee State University en_US dc.thesis.degreelevel Masters en_US dc.title Lattice Structures in Finite Graph Topologies en_US dc.type Thesis en_US
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