Shen, Yingyi2012-04-262012-04-262012-04-26https://hdl.handle.net/10161/5237This thesis studies properties of edge toric ideals and resolutions by analyzing the associated graphs of algebraic structures. It mainly focused on proving that the repeated edges in a graph wouldn't change some properties of its underlying algebraic structure. An application of this result is that when we study multi-edge graphs, we can simplify in nite numbers of graphs to a simple one by deleting all the repeated edges.en-USCommutative AlgebraMathematicsGraphIdealHonors thesis