[Nauty] Generate all non-isomorphic graphs without edges between the last k vertices

[mskala at ansuz.sooke.bc.ca]

On Thu, 13 Jun 2019, Andy Mercer wrote:
> What do you mean by "no edges within the subset of vertices > k "?  Do you
> want all non-isomorphic graphs on N vertices having at  least k isolated nodes
> (at least k nodes of degree zero)?

An edge "within" a subset of vertices means an edge with both endpoints in
the subset.  So my reading of the desired condition is that the vertices
with indices >k are not necessarily isolated vertices - they might have
edges to other vertices with indices at most k - but the subgraph
induced by the set of vertices with indices >k contains no edges.

I doubt that geng can do this all by itself.  Depending on the scale of
the project (size of graphs, number of them, how often I wanted to do this
kind of generation) I'd be inclined to either write a filter program for
geng's output to pass only the desired graphs, or go all the way to
writing my own generator program; it wouldn't be hard to tweak the orderly
generation framework to do similar filtering on the fly.

-- 
Matthew Skala
mskala at ansuz.sooke.bc.ca                 People before tribes.
https://ansuz.sooke.bc.ca/