to my knowledge nothing like this has been created yet. I know that programs that solve math equations are few and far between. Likely because most math people can program as well. However, to my knowledge thus far no such programs exist.
Are there any graph theory problems that could be solved by a lone, run-of-the-mill computer programmer as a side hobby?
I am thinking of a modest app that allows a simple graph to be drawn, and a selection of properties that can be searched for in the on-screen graph, e.g., bipartite, hasClique, etc.
If enough of these properties can be implemented, then collections of properties could be sought.
Eventually there would be an algorithm(s) to gradually construct graphs, and at each iteration in the construction process, some collection of properties can be sought for in the graph so far.
My question is has all this been done already by teams of commercial programmers, so that, at best this would just be self-educational?
My advice would be: Review a few texts on discrete math and see what is common among them for topics of you might consider to be graph theory.
Commercial products are probably either (1) dedicated to a specific class of problems or (2) academic and related to specific algorithms.
If you plan to write to sell, you may sell a few but obviously the market is saturated with high-power math programs. For me, I don't have the funds to purchase what I want and I would not use such software to educate my daughter. It is usually possible to input data and not understand either the process by which the answer was arrived at or even if it is correct. So from my point of view, I would have no use for it.
If on the other hand the software explained step-by-step (i.e., educational software) it might be useful in my current situation, and to others who are educating themselves or other persons.
Teaching or exploring math primarily by using software is completely different than doing the same by hand and mind alone. I find it more useful to go the latter route because that is where my current interests lie.
To paraphrase a common cliche, "To someone whose only tool is graph theory, every problem appears to be solvable by graph theory."
If you want to write a general tool for checking homework, that would be the way to go. You would also want to specify that user-defined parameters could be either with calculus or without calculus; that would attract a wider range of students.