Neufeld, Eugene Trivan2024-08-152024-08-1519931993https://hdl.handle.net/1828/19110A torus is a sphere with one handle. A toroidal graph is one that can be embedded in the torus with no overlapping edges. Although various theoretically efficient algo­rithms for testing toroidality of graphs have been published, none is claimed to be "practical". We develop an exponential toroidality tester that is practical enough to compute the minor order obstructions to toroidality on up to ten vertices and which gives indications that there are several thousand of these obstructions all together. We validate the algorithm combinatorially, and discuss prospects of improvements in efficiency.129 pagesAvailable to the World Wide WebUN SDG 7: Affordable and Clean EnergyThesis