Patrick Gaskill called the code for the conjecturing module of our Independence Number Project Graph Brain. Nico and I have one growing file (gt.py) with all the graph invariants, graph properties and graph objects used for making graph conjectures, which can be found on Github. We would ideally like to include all published graph invariants, graph properties and graph objects in this file. Graph Brain seems like a great name to repurpose for this project.
I have an intention in the next year to add lots more graphs, invariants and properties. I’m curious to see what kinds of conjectures we get as we add more and more knowledge to the program. It would be even better if students and others contributed even more graphs, invariants and properties – to have a community effort, at least for graph theory. Of course, this idea could be duplicated for any other object type. Getting a critical mass of ingredients may be the secret to getting the most useful conjectures.
I gave a talk on the program at Johns Hopkins University today and got lots of great questions, comments and suggestions. Tamas Budavari suggested or gave me the idea of having a web page or public interface to make it easy for others to add new graphs, invariants and properties. Wow, that would be great. There are so many interesting things to do!