I am interested in generating all possible non-isomorphic vertex cuts of a given size for a particular family of graphs. The graphs are regular, vertex transitive, and edge transitive.
My main purpose for asking is to investigate the toughness of this family of graphs by calculating the number of components in the $G \setminus S$, where $S$ is a vertex cut. However, given the graph's properties, there is bound to be a lot of overlap in isomorphic vertex cuts, and thus repeated calculations, which I am looking to eliminate.
I've done a fair amount of searching on the web, Arxiv, and Google Scholar, but all the algorithms I am able to find focus on minimum vertex cuts, whereas I am interested in cuts of a given size that may not be minimal.
Thank you for any help you can provide!