Honors Thesis Presentation: Generating Graphs up to the Action of Finite Groups

Abstract: We describe a general approach for exhaustively enumerating representatives for isomorphism classes of families of graphs without generating isomorphic duplicates at any intermediate step. Here an isomorphism class is taken to mean an orbit of a finite group acting on the vertices of graphs, where the group may be given only through a set of generators. The approach outlined, however, is applicable to essentially any type of combinatorial object that could be constructed from sub-objects and where such a notion of isomorphism exists. We then apply this approach to study the homology groups of the Matching complex.

Advisor: John Shareshian